Add Batch b877dc40-19e2-4370-8dc4-3624ceb211dd data

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@@ -679,3 +679,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2025/DiffusionDrive_ Truncated Diffusion Model for End-to-End Autonomous Driving/186eb20a-812b-4b73-a9f1-a45f01468323_content_list.json

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+        "text": "Bencheng Liao $^{1,2,\\diamond}$  Shaoyu Chen $^{2,3}$  Haoran Yin $^{3}$  Bo Jiang $^{2,\\diamond}$  Cheng Wang $^{1,2,\\diamond}$  Sixu Yan $^{2}$  Xinbang Zhang $^{3}$  Xiangyu Li $^{3}$  Ying Zhang $^{3}$  Qian Zhang $^{3}$  Xinggang Wang $^{2}$ $^{1}$  Institute of Artificial Intelligence, Huazhong University of Science & Technology  \n $^{2}$  School of EIC, Huazhong University of Science & Technology  \n $^{3}$  Horizon Robotics  \nCode & Model & Demo: hustvl/DiffusionDrive",
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+        "text": "Recently, the diffusion model has emerged as a powerful generative technique for robotic policy learning, capable of modeling multi-mode action distributions. Leveraging its capability for end-to-end autonomous driving is a promising direction. However, the numerous denoising steps in the robotic diffusion policy and the more dynamic, open-world nature of traffic scenes pose substantial challenges for generating diverse driving actions at a real-time speed. To address these challenges, we propose a novel truncated diffusion policy that incorporates prior multi-mode anchors and truncates the diffusion schedule, enabling the model to learn denoising from anchored Gaussian distribution to the multi-mode driving action distribution. Additionally, we design an efficient cascade diffusion decoder for enhanced interaction with conditional scene context. The proposed model, DiffusionDrive, demonstrates  $10 \\times$  reduction in denoising steps compared to vanilla diffusion policy, delivering superior diversity and quality in just 2 steps. On the planning-oriented NAVSIM dataset, with aligned ResNet-34 backbone, DiffusionDrive achieves 88.1 PDMS without bells and whistles, setting a new record, while running at a real-time speed of 45 FPS on an NVIDIA 4090. Qualitative results on challenging scenarios further confirm that DiffusionDrive can robustly generate diverse plausible driving actions.",
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+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "End-to-end autonomous driving has gained significant attention in recent years due to advancements in perception models (detection [5, 17, 24, 42], tracking [54-56], online mapping [27, 28, 32], etc.), which directly learns the driving policy from the raw sensor inputs. This data-driven ap",
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+            "Figure 1. The comparison of different end-to-end paradigms. (a) Single mode regression [8, 16, 20]. (b) Sampling from vocabulary [4, 25]. (c) Vanilla diffusion policy [7, 19]. (d) The proposed truncated diffusion policy."
+        ],
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+        "type": "text",
+        "text": "proach offers a scalable and robust alternative to traditional rule-based motion planning, which often struggles to generalize to complex real-world driving settings.",
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+        "text": "To effectively learn from data, mainstream end-to-end planners (e.g., Transfuser [8], UniAD [16], VAD [20]) typically regress a single-mode trajectory from an ego-query as shown in Fig. 1a. However, this paradigm does not account for the inherent uncertainty and multi-mode nature of driving behaviors. Recently, VADv2 [20] introduces a large fixed vocabulary of anchor trajectories (4096 anchors) to discretize the continuous action space and capture a broader range of driving behaviors, and then samples from these anchors based on predicted scores as shown in Fig. 1b. However, this large fixed-vocabulary paradigm is fundamentally constrained by the number and quality of anchor trajectories, often failing in out-of-vocabulary scenarios. Furthermore, managing a large number of anchors presents significant computational challenges for real-time applications. Rather than discretizing the action space, diffusion model [7] has proven to be a powerful genera",
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+    {
+        "type": "header",
+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "To distinguish the term \"multimodal\" used to describe input data, we use \"multi-mode\" in this paper to refer to diverse planning decisions.",
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+        "type": "page_footnote",
+        "text": "$\\diamond$  Intern of Horizon Robotics;  $\\boxtimes$  Corresponding author: Xinggang Wang (xgwang@hust.edu.cn).",
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+        "type": "page_number",
+        "text": "12037",
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+    {
+        "type": "text",
+        "text": "tive decision-making policy in the robotics domain, which can directly sample multi-mode physically plausible actions from a Gaussian distribution via iterative denoising process.",
+        "bbox": [
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+        "text": "This inspires us to replicate the success of the diffusion model in the robotics domain to end-to-end autonomous driving. We apply the vanilla robotic diffusion policy to the well-known single-mode-regression method, Transfuser [8], by proposing a variant,  $\\text{Transfuser}_{\\text{DP}}$ , which replaces the deterministic MLP regression head with a conditional diffusion model [34]. Though  $\\text{Transfuser}_{\\text{DP}}$  improves planning performance, two major issues arise: 1) The numerous 20 denoising steps in the vanilla DDIM diffusion policy introduce heavy computational consumption during inference as shown in Tab. 2, hindering the real-time application for autonomous driving. 2) The trajectories sampled from different Gaussian noises severely overlap with each other, as illustrated in Fig. 2. This underscores the non-trivial challenge of taming the diffusion models for the dynamic and open-world traffic scenes.",
+        "bbox": [
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+        "type": "text",
+        "text": "Unlike the vanilla diffusion policy, which samples actions from a random Gaussian noise conditioned on scene context, human drivers adhere to established driving patterns that they dynamically adjust in response to real-time traffic conditions. This insight motivates us to embed these prior driving patterns into the diffusion policy by partitioning the Gaussian distribution into multiple sub-Gaussian distributions centered around prior anchors, referred to as anchored Gaussian distribution. It is implemented by truncating the diffusion schedule to introduce a small portion of Gaussian noise around the prior anchors as shown in Fig. 3. Thanks to the multi-mode distributional expressivity of the diffusion model, the proposed truncated diffusion policy effectively covers the potential action space without requiring a large set of fixed anchors, as VADv2 does. With more reasonable initial noise samples from the anchored Gaussian distribution, we can truncate the denoising process, reducing the required steps from 20 to just 2—a substantial speedup that satisfies the real-time requirements of autonomous driving.",
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+        "type": "text",
+        "text": "To enhance the interaction with conditional scene context, we propose an efficient transformer-based diffusion decoder that interacts not only with structured queries from the perception module but also with Bird's Eye View (BEV) and perspective view (PV) features through a sparse deformable attention mechanism [3, 62]. Additionally, we introduce a cascade mechanism to iteratively refine the trajectory reconstruction within the diffusion decoder at each denoising step.",
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+        "type": "text",
+        "text": "With these innovations, we present DiffusionDrive, a diffusion model for real-time end-to-end autonomous driving. We benchmark our method on the planning-oriented NAVSIM dataset [11] using non-reactive simulation and closed-loop evaluations. Without bells and whis",
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+        "text": "tles, DiffusionDrive achieves 88.1 PDMS on NAVSIM navtest split with the aligned ResNet-34 backbone, significantly outperforming previous state-of-the-art methods. Even compared to the NAVSIM challenge-winning solution Hydra-MDP- $\\nu_{8192}$ -W-EP [25], which follows VADv2 with 8192 anchor trajectories and further incorporates post-processing and additional supervision, DiffusionDrive still outperforms it by 1.6 PDMS through directly learning from human demonstrations and inferring without post-processing, while running at real-time speed of 45 FPS on an NVIDIA 4090. We further validate the superiority of DiffusionDrive on popular nuScenes dataset [2] with open-loop evaluations, DiffusionDrive runs  $1.8 \\times$  faster than VAD and outperforms it [20] by  $20.8\\%$  lower L2 error and  $63.6\\%$  lower collision rate with the same ResNet-50 backbone, demonstrating state-of-the-art planning performance.",
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+        "type": "text",
+        "text": "Our contributions can be summarized as follows:",
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+        "list_items": [
+            "- We firstly introduce the diffusion model to the field of end-to-end autonomous driving and propose a novel truncated diffusion policy to address the issues of mode collapse and heavy computational overhead found in direct adaptation of vanilla diffusion policy to the traffic scene.",
+            "- We design an efficient transformer-based diffusion decoder that interacts with the conditional information in a cascaded manner for better trajectory reconstruction.",
+            "- Without bells and whistles, DiffusionDrive significantly outperforms previous state-of-the-art methods, achieving a record-breaking 88.1 PDMS on the NAVSIM navtest split with the same backbone, while maintaining real-time performance at 45 FPS on an NVIDIA 4090.",
+            "- We qualitatively demonstrate that DiffusionDrive can generate more diverse and plausible trajectories, exhibiting high-quality multi-mode driving actions in various challenging scenarios."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "End-to-end autonomous driving. UniAD [16], as a pioneering work, demonstrates the potential of end-to-end autonomous driving by integrating multiple perception tasks to enhance planning performance. VAD [20] further explores the use of compact vectorized scene representations to improve efficiency. Subsequently, a series of works [6, 8, 12, 23, 26, 43, 45, 58] have adopted the single-trajectory planning paradigm to enhance planning performance further. More recently, VADv2 [4] shifts the paradigm towards multi-mode planning by scoring and sampling from a large fixed vocabulary of anchor trajectories. Hydra-MDP [25] improves the scoring mechanism of VADv2 by introducing extra supervision from a rule-based scorer. SparseDrive [39] explores an alternative BEV-free solution. Unlike existing multi-mode planning approaches, we propose a novel paradigm that leverages powerful generative diffusion models for end-to-end autonomous driving.",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "12038",
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+        "page_idx": 1
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+    {
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+        "img_path": "images/eae6cbced2a079f01e0437de2d3082d21ee7f04b1c9e9400b61c9f8776e04382.jpg",
+        "image_caption": [
+            "(b) Top-1's turning left and diverse top-10's lane changing.",
+            "Figure 2. Qualitative comparison of Transfuser, TransfuserDP and DiffusionDrive on challenging scenes of NAVSIM navtest split. With the same inputs from front cameras and LiDAR, DiffusionDrive achieves the highest planning quality of top-1 scoring trajectory as illustrated in Tab. 2. We render the highlighted diverse trajectories predicted by DiffusionDrive in the front view. (a) and (b) shows that the top-1 scoring trajectory of DiffusionDrive closely matches the ground truth for both going straight and turning left. Additionally, DiffusionDrive's top-10 scoring trajectory demonstrates high-quality lane changing—an ability not observed in multi-mode TransfuserDP and impossible for Transfuser."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Diffusion model for traffic simulation. Driving diffusion policy has been explored in the traffic simulation by leveraging only abstract perception groundtruth [9, 18, 21, 44]. MotionDiffuser [21] and CTG [60] are pioneering applications of diffusion models for multi-agent motion prediction, using a conditional diffusion model to sample target trajectories from Gaussian noise.  $\\mathrm{CTG + + }$  [59] further incorporates a large language model (LLM) for language-driven guidance, improving usability and enabling realistic traffic simulations. Diffusion-ES [48] replaces reward-gradient-guided denoising with evolutionary search. Moving beyond diffusion models limited to traffic simulation with perception groundtruth, our approach unlocks the potential of dif",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "fusion models for real-time, end-to-end autonomous driving through our proposed truncated diffusion policy and efficient diffusion decoder.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Diffusion model for robotic policy learning. Diffusion policy [7] demonstrates the great potential in robotic policy learning, effectively capturing multi-mode action distributions and high-dimensional action spaces. Diffuser [19] proposes an unconditional diffusion model for trajectory sampling, incorporating techniques such as classifier-free guidance and image inpainting to achieve guided sampling. Subsequently, numerous works have applied diffusion models to various robotic tasks, including stationary manipulation [1, 53], mobile manipulation [47], autonomous nav",
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+        "text": "12039",
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+    {
+        "type": "text",
+        "text": "Diffusion step:  $q(\\tau^i |\\tau^{i - 1}),i\\in [1,T]$",
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/8cfefc6af824cac1c473f324a6793a77eea43f897f66e0c85228a8fc8fda716a.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "Denoising step:  $p_{\\theta}\\big(\\tau^i |\\tau^{i - 1},z\\big),i\\in [1,T]$",
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+    {
+        "type": "text",
+        "text": "Vanilla Diffusion Policy vs. Truncated Diffusion Policy (ours)",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Diffusion step:  $q(\\tau^i |\\tau^{i - 1}),i\\in [1,T_{\\mathrm{trunc}}]$",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/908ca90015f3cdef9e8a7a268d4d0e4dffad49b35c5355a18d9a23521945317e.jpg",
+        "image_caption": [
+            "Adding noise to the anchors with truncated diffusion schedule."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Denosing from anchored Gaussian distribution with fewer steps.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/90462a069ee2704c6c9619343f1e37dcc31b96ef9d735cc9113ee30ae82e944a.jpg",
+        "image_caption": [
+            "Denoising step:  $p_{\\theta}(\\tau^i |\\tau^{i - 1},z),i\\in [1,T_{\\mathrm{trunc}}]$",
+            "Figure 3. Illustration of truncated diffusion policy by comparing with vanilla diffusion policy. We truncate the diffusion process and only add a small portion of Gaussian noise to diffuse the anchor trajectories. Then, we train the diffusion model to reconstruct the ground-truth trajectory from the anchored Gaussian distribution with conditional scene context. During the inference, we also truncate the denoising process by starting from the better samples in the anchored Gaussian distribution than the pure Gaussian noise."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "igation [37, 51], quadruped locomotion [38], and dexterous manipulation [46]. However, directly applying vanilla diffusion policy to end-to-end autonomous driving poses unique challenges, as it requires real-time efficiency and the generation of plausible multi-mode trajectories in dynamic and open-world traffic scenes. In this work, we propose a novel truncated diffusion policy to address these challenges, introducing concepts that have not yet been explored in the robotics field.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Diffusion model for image generation. Diffusion models have been extensively adopted for image generation tasks [33, 36, 49, 50, 61]. DDIM [35] enhances DDPM [14] by enabling efficient sampling with significantly fewer steps based on non-Markovian diffusion processes. Flow matching [30, 31] further optimizes the generative process by directly modeling continuous probability flows. TDPM [57] proposes truncated denoising, which initiates the generation process from an implicit intermediate distribution to accelerate sampling. In contrast to these approaches, our method introduces an explicit driving prior within the diffusion policy, effectively guiding the diffusion process toward more accurate and efficient generation tailored specifically for end-to-end autonomous driving.",
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Preliminary",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Task formulation. End-to-end autonomous driving takes raw sensor data as input and predicts the future trajectory of the ego-vehicle. The trajectory is represented as a sequence of waypoints  $\\tau = \\{(x_{t},y_{t})\\}_{t = 1}^{T_{f}}$ , where  $T_{f}$  denotes the planning horizon, and  $(x_{t},y_{t})$  is the location of each waypoint at time  $t$  in the current ego-vehicle coordinate system.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Conditional diffusion model. The conditional diffusion model poses a forward diffusion process as gradually adding noise to the data sample, which can be defined as:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(\\tau^ {i} \\mid \\tau^ {0}\\right) = \\mathcal {N} \\left(\\tau^ {i}; \\sqrt {\\bar {\\alpha} ^ {i}} \\boldsymbol {\\tau} ^ {0}, \\left(1 - \\bar {\\alpha} ^ {i}\\right) \\mathbf {I}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau^0$  is the clean data sample, and  $\\tau^i$  is the data sample with noise at time  $i$  (Note: we use superscript  $i$  to denote diffusion timestep). The constant  $\\bar{\\alpha}^i = \\prod_{s=1}^i \\alpha^s = \\prod_{s=1}^i (1 - \\beta^s)$  and  $\\beta^s$  is the noise schedule. We train the reverse process model  $f_\\theta(\\tau^i, z, i)$  to predict  $\\tau^0$  from  $\\tau^i$  with the guidance of conditional information  $z$ , where  $\\theta$  is the trainable model parameter. During inference, the trained diffusion model  $f_\\theta$  progressively refines from the random",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12040",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/39188c906af22969f52df93d3eccb03e17c013632528cf929e933086a49a30e7.jpg",
+        "image_caption": [
+            "Figure 4. Overall architecture of DiffusionDrive. (a) DiffusionDrive can integrate various existing perception modules and sensor inputs. (b) The designed diffusion decoder takes the sampled noisy trajectories from anchored Gaussian distribution as input and progressively denoises them with enhanced interactions with the conditional scene context in a cascade manner to generate the final predictions."
+        ],
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/3501d4a7121777ea39ebdd62ca4e2b3efafa5c0f6dd4428085611e154596d12e.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "text",
+        "text": "noise  $\\tau^T$  sampled in Gaussian distribution to the predicted clean data sample  $\\tau^0$  with the guidance of conditional information  $z$ , which is defined as:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} \\mid z\\right) = \\int p \\left(\\boldsymbol {\\tau} ^ {T}\\right) \\prod_ {i = 1} ^ {T} p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {i - 1} \\mid \\boldsymbol {\\tau} ^ {i}, z\\right) d \\boldsymbol {\\tau} ^ {1: T}. \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "3.2. Investigation",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Turn Transfuser [8] into conditional diffusion model. We begin from the representative deterministic end-to-end planner Transfuser [8] and turn it into a generative model  $\\mathrm{Transfuser}_{\\mathrm{DP}}$  by simply replacing the regression MLP layers with the conditional diffusion model UNet following vanilla diffusion policy [7]. During the evaluation, we sample a random noise and progressively refine it with 20 steps. Tab. 2 shows that  $\\mathrm{Transfuser}_{\\mathrm{DP}}$  achieves better planning quality than deterministic Transfuser.",
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+    {
+        "type": "text",
+        "text": "Mode collapse. To further investigate the multi-mode property of the vanilla diffusion policy in driving, we sampled 20 random noises from Gaussian distribution and denoised them using 20 steps. As shown in Fig. 2, the different random noises converge to similar trajectories after the denoising process. To quantitatively analyze the phenomenon of mode collapse, we define a mode diversity score  $\\mathcal{D}$  based on the mean Intersection over Union (mIoU) between each denoised trajectory and the union of all denoised trajectories:",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} = 1 - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {\\operatorname {A r e a} \\left(\\tau_ {i} \\cap \\bigcup_ {j = 1} ^ {N} \\tau_ {j}\\right)}{\\operatorname {A r e a} \\left(\\tau_ {i} \\cup \\bigcup_ {j = 1} ^ {N} \\tau_ {j}\\right)}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            158,
+            729,
+            482,
+            772
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau_{i}$  represents the  $i$ -th denoised trajectory,  $N$  is the total number of sampled trajectories and  $\\bigcup_{j=1}^{N} \\tau_{j}$  is the union of all denoised trajectories. A higher mIoU indicates less diversity of the denoised trajectories. The quantitative mode diversity results in Tab. 2 further validate the observations presented in Fig. 2.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Heavy denoising overhead. The DDIM [35] diffusion policy requires 20 denoising steps to transform random noise",
+        "bbox": [
+            89,
+            869,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "into a feasible trajectory, which introduces significant computational overhead, reducing the FPS from 60 to 7, as shown in Tab. 2, and making it impractical for real-time online driving applications.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Truncated Diffusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Human driving follows fixed patterns, unlike the random noise denoising in vanilla diffusion policy. Motivated by this, we propose a truncated diffusion policy that begins the denoising process from an anchored Gaussian distribution instead of a standard Gaussian distribution. To enable the model to learn to denoise from the anchored Gaussian distribution to the desired driving policy, we further truncate the diffusion schedule during training, adding only a small amount of Gaussian noise to the anchors.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Training. We first construct the diffusion process by adding Gaussian noise to anchors  $\\{\\mathbf{a}_k\\}_{k=1}^{N_{\\text{anchor}}}$  clustered by K-Means on the training set, where  $\\mathbf{a}_k = \\{(x_t, y_t)\\}_{t=1}^{T_f}$ . We truncate the diffusion noise schedule to diffuse the anchors to the anchored Gaussian distribution:",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tau_ {k} ^ {i} = \\sqrt {\\bar {\\alpha} ^ {i}} \\mathbf {a} _ {k} + \\sqrt {1 - \\bar {\\alpha} ^ {i}} \\boldsymbol {\\epsilon}, \\quad \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I}), \\qquad (4)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            628,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $i \\in [1, T_{\\mathrm{trunc}}]$  and  $T_{\\mathrm{trunc}} \\ll T$  is the truncated diffusion steps.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During training, the diffusion decoder  $f_{\\theta}$  takes as input  $N_{\\mathrm{anchor}}$  noisy trajectories  $\\{\\tau_k^i\\}_{k=1}^{N_{\\mathrm{anchor}}}$  and predicts classification scores  $\\{\\hat{s}_k\\}_{k=1}^{N_{\\mathrm{anchor}}}$  and denoised trajectories  $\\{\\hat{\\tau}_k\\}_{k=1}^{N_{\\mathrm{anchor}}}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{\\hat {s} _ {k}, \\hat {\\tau} _ {k} \\right\\} _ {k = 1} ^ {N _ {\\text {a n c h o r}}} = f _ {\\theta} \\left(\\left\\{\\tau_ {k} ^ {i} \\right\\} _ {k = 1} ^ {N _ {\\text {a n c h o r}}}, z\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            594,
+            744,
+            906,
+            766
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $z$  represents the conditional information. We assign the noisy trajectory around the closest anchor to the ground truth trajectory  $\\tau_{\\mathrm{gt}}$  as positive sample  $(y_k = 1)$  and others as negative samples  $(y_k = 0)$ . The training objective combines trajectory reconstruction and classification:",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\sum_ {k = 1} ^ {N _ {\\text {a n c h o r}}} \\left[ y _ {k} \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\tau} _ {k}, \\tau_ {\\mathrm {g t}}\\right) + \\lambda \\mathrm {B C E} \\left(\\hat {s} _ {k}, y _ {k}\\right) \\right], \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            562,
+            862,
+            905,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "12041",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/e45249461eb686dfd45a7e9e800e8405ad0142b839ff26eadf7d5daf32e7d80d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Input</td><td>Img. Backbone</td><td>Anchor</td><td>NC↑</td><td>DAC ↑</td><td>TTC ↑</td><td>Comf. ↑</td><td>EP ↑</td><td>PDMS ↑</td></tr><tr><td>UniAD [16]</td><td>Camera</td><td>ResNet-34 [13]</td><td>0</td><td>97.8</td><td>91.9</td><td>92.9</td><td>100</td><td>78.8</td><td>83.4</td></tr><tr><td>PARA-Drive [45]</td><td>Camera</td><td>ResNet-34 [13]</td><td>0</td><td>97.9</td><td>92.4</td><td>93.0</td><td>99.8</td><td>79.3</td><td>84.0</td></tr><tr><td>LTF [8]</td><td>Camera</td><td>ResNet-34 [13]</td><td>0</td><td>97.4</td><td>92.8</td><td>92.4</td><td>100</td><td>79.0</td><td>83.8</td></tr><tr><td>Transfuser [8]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>0</td><td>97.7</td><td>92.8</td><td>92.8</td><td>100</td><td>79.2</td><td>84.0</td></tr><tr><td>DRAMA [52]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>0</td><td>98.0</td><td>93.1</td><td>94.8</td><td>100</td><td>80.1</td><td>85.5</td></tr><tr><td>VADv2- \\( \\mathcal{V}_{8192} \\) [4]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>8192</td><td>97.2</td><td>89.1</td><td>91.6</td><td>100</td><td>76.0</td><td>80.9</td></tr><tr><td>Hydra-MDP- \\( \\mathcal{V}_{8192} \\) [25]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>8192</td><td>97.9</td><td>91.7</td><td>92.9</td><td>100</td><td>77.6</td><td>83.0</td></tr><tr><td>Hydra-MDP- \\( \\mathcal{V}_{8192} \\)-W-EP [25]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>8192</td><td>98.3</td><td>96.0</td><td>94.6</td><td>100</td><td>78.7</td><td>86.5</td></tr><tr><td>DiffusionDrive (Ours)</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>20</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr></table>",
+        "bbox": [
+            93,
+            88,
+            903,
+            262
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/90d41fde76a17be1cc5e9e996a65b8c2f21cc99ab9cbe1617e0483aabeced382.jpg",
+        "table_caption": [
+            "Table 1. Comparison on planning-oriented NAVSIM navtest split with closed-loop metrics. “C & L” denotes the use of both camera and LiDAR as sensor inputs. “ $\\mathcal{V}_{8192}$ ” denotes 8192 anchors. “Hydra-MDP- $\\mathcal{V}_{8192}$ -W-EP” is a variant of Hydra-MDP [25], which is further trained to fit the EP evaluation metric with additional supervision from the rule-based evaluator and uses weighted confidence post-processing. DiffusionDrive simply learns from human demonstrations and infers without post-processing. The best and the second best results are denoted by bold and underline."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">NC↑</td><td rowspan=\"2\">DAC↑</td><td rowspan=\"2\">TTC↑</td><td rowspan=\"2\">Comf.↑</td><td rowspan=\"2\">EP↑</td><td rowspan=\"2\">PDMS↑</td><td rowspan=\"2\">Arch.</td><td colspan=\"3\">Plan Module Time</td><td rowspan=\"2\">Total ↓</td><td rowspan=\"2\">D↑</td><td rowspan=\"2\">Para.↓</td><td rowspan=\"2\">FPS↑</td></tr><tr><td>Step Time↓</td><td>Steps ↓</td><td></td></tr><tr><td>Transfuser</td><td>97.7</td><td>92.8</td><td>92.8</td><td>100</td><td>79.2</td><td>84.0</td><td>MLP</td><td>0.2ms</td><td>1</td><td>0.2ms</td><td>0%</td><td>56M</td><td>60</td><td></td></tr><tr><td>TransfuserDP</td><td>97.5</td><td>93.7</td><td>92.7</td><td>100</td><td>79.4</td><td>84.6+0.6</td><td>UNet</td><td>6.5ms</td><td>20</td><td>130.0ms</td><td>11%</td><td>101M</td><td>7</td><td></td></tr><tr><td>TransfuserTD</td><td>97.9</td><td>94.2</td><td>93.9</td><td>100</td><td>80.2</td><td>85.7+1.7</td><td>UNet</td><td>6.9ms</td><td>2</td><td>13.8ms</td><td>70%</td><td>102M</td><td>27</td><td></td></tr><tr><td>DiffusionDrive</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1+4.1</td><td>Dec.</td><td>3.8ms</td><td>2</td><td>7.6ms</td><td>74%</td><td>60M</td><td>45</td><td></td></tr></table>",
+        "bbox": [
+            94,
+            334,
+            897,
+            438
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Roadmap from Transfuser to DiffusionDrive on NAVSIM navtest split. \"TransfuserDP\" denotes Transfuser with vanilla DDIM diffusion policy [7]. \"TransfuserTD\" denotes Transfuser with truncated diffusion policy. \"Step Time\" denotes the runtime of each denoising step. \"FPS\" and runtime are measured on an NVIDIA 4090 GPU. \"D\" denotes the mode diversity score defined in Eq. (3).",
+        "bbox": [
+            89,
+            439,
+            906,
+            484
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  balances the simple L1 reconstruction loss  $\\mathcal{L}_{\\mathrm{rec}}$  and binary cross-entropy (BCE) classification loss.",
+        "bbox": [
+            89,
+            487,
+            482,
+            517
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Inference. We use a truncated denoising process that starts with noisy trajectories sampled from the anchored Gaussian distribution and progressively denoises them to final predictions. At each denoising timestep, the estimated trajectories from the previous step are passed to the diffusion decoder  $f_{\\theta}$ , which predicts classification scores  $\\{\\hat{s}_k\\}_{k=1}^{N_{\\mathrm{infer}}}$  and coordinates  $\\{\\hat{\\tau}_k\\}_{k=1}^{N_{\\mathrm{infer}}}$ . After obtaining the current timestep's predictions, we apply the DDIM [35] update rule to sample trajectories for the next timestep.",
+        "bbox": [
+            89,
+            518,
+            482,
+            656
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Inference flexibility. A key advantage of our approach lies in its inference flexibility. While the model is trained with  $N_{\\text{anchor}}$  trajectories, the inference process can accommodate an arbitrary number of trajectory samples  $N_{\\text{infer}}$ , where  $N_{\\text{infer}}$  can be dynamically adjusted based on computational resources or application requirements.",
+        "bbox": [
+            89,
+            657,
+            482,
+            750
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4. Architecture",
+        "text_level": 1,
+        "bbox": [
+            89,
+            756,
+            225,
+            770
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The overall architecture of our proposed method, DiffusionDrive, is illustrated in Fig. 4. DiffusionDrive can integrate various existing perception modules used in previous end-to-end planners [8, 16, 20, 39] and take different sensor inputs. The designed diffusion decoder is tailored for the complex and challenging driving application, which has enhanced interactions with the conditional scene context.",
+        "bbox": [
+            89,
+            777,
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+            883
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Diffusion decoder. Given the set of sampled noisy trajectories",
+        "bbox": [
+            89,
+            885,
+            482,
+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ries  $\\{\\hat{\\tau}_k\\}_{k=1}^{N_{\\mathrm{infer}}}$  from the anchored Gaussian distribution, we begin by applying deformable spatial cross-attention [29, 42, 62] to interact with Bird's Eye View (BEV) or Perspective View (PV) features based on the trajectory coordinates. Subsequently, cross-attention is performed between the trajectory features and the agent/map queries derived from the perception module, followed by a feed-forward network (FFN). To encode the diffusion timestep information, we utilize a Timestep Modulation layer, which is followed by a Multi-Layer Perceptron (MLP) that predicts the confidence score and the offset relative to the initial noisy trajectory coordinates. The output from this diffusion decoder layer serves as the input for the subsequent cascade diffusion decoder layer. DiffusionDrive further reuses the cascade diffusion decoder to iteratively denoise the trajectory during inference, with parameters shared across the different denoising timesteps. The final trajectory with the highest confidence score is selected as the output.",
+        "bbox": [
+            511,
+            486,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiment",
+        "text_level": 1,
+        "bbox": [
+            511,
+            773,
+            638,
+            792
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Dataset",
+        "text_level": 1,
+        "bbox": [
+            511,
+            800,
+            609,
+            814
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "NAVSIM. The NAVSIM dataset [11] is a real-world planning-oriented dataset builds upon OpenScene [10], a compact redistribution of nuPlan [22], the largest publicly available annotated driving dataset. NAVSIM leverages eight cameras to achieve a full  $360^{\\circ}$  FOV, along with a",
+        "bbox": [
+            511,
+            824,
+            906,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "12042",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/5d60719ec93c39d85aaf432bb11752b22d4eff87f1347e8e26a027665583c888.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">ID</td><td rowspan=\"2\">UNet Decoder</td><td rowspan=\"2\">Ego Query Interaction</td><td rowspan=\"2\">Spatial Cross-attn</td><td rowspan=\"2\">Agent/Map Cross-attn</td><td rowspan=\"2\">Cascade Decoder</td><td rowspan=\"2\">Param.↓</td><td rowspan=\"2\">NC↑</td><td rowspan=\"2\">DAC↑</td><td colspan=\"4\">Planning Metric</td><td rowspan=\"2\">PDMS↑</td></tr><tr><td>TTC↑</td><td>Comf.↑</td><td>EP↑</td><td></td></tr><tr><td>1</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>102M</td><td>97.9</td><td>94.2</td><td>93.9</td><td>100</td><td>80.2</td><td></td><td>85.7</td></tr><tr><td>2</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>57M</td><td>88.7</td><td>83.2</td><td>80.0</td><td>84.8</td><td>43.3</td><td></td><td>55.1</td></tr><tr><td>3</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>58M</td><td>98.2</td><td>95.4</td><td>94.4</td><td>100</td><td>81.3</td><td></td><td>87.1</td></tr><tr><td>4</td><td>X</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>58M</td><td>97.9</td><td>93.5</td><td>93.8</td><td>100</td><td>79.8</td><td></td><td>85.1</td></tr><tr><td>5</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>59M</td><td>98.0</td><td>95.8</td><td>94.4</td><td>100</td><td>81.7</td><td></td><td>87.4</td></tr><tr><td>6</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td></td><td>88.1</td></tr></table>",
+        "bbox": [
+            93,
+            88,
+            903,
+            229
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/8d14f9f0b1907f2e1c1f24a3c9ffc59f48c791507d86b6b15ede4856c841428c.jpg",
+        "table_caption": [
+            "Table 3. Ablation for design choices. \"Cascade Decoder\" indicates that we stack 2 cascade diffusion decoder layers. ID-1 refers to TransfuserTD in Tab. 2, utilizing conditional UNet and interaction with the ego-query, which Transfuser uses to directly regress the single-mode trajectory."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Steps</td><td>Param.</td><td>NC</td><td>DAC</td><td>TTC</td><td>Comf.</td><td>EP</td><td>PDMS</td></tr><tr><td>1</td><td>60M</td><td>98.3</td><td>96.0</td><td>94.7</td><td>100</td><td>82.1</td><td>87.9</td></tr><tr><td>2</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr><tr><td>3</td><td>60M</td><td>98.2</td><td>96.3</td><td>94.7</td><td>100</td><td>92.2</td><td>88.1</td></tr></table>",
+        "bbox": [
+            93,
+            277,
+            356,
+            335
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/dfbc91c12c6096eb2909c06a78669315159466720a4e4cce73d6cba83ba5ad34.jpg",
+        "table_caption": [
+            "Table 4. Denoising step number."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Stages</td><td>Param.</td><td>NC</td><td>DAC</td><td>TTC</td><td>Comf.</td><td>EP</td><td>PDMS</td></tr><tr><td>1</td><td>59M</td><td>98.0</td><td>95.8</td><td>94.4</td><td>100</td><td>81.7</td><td>87.4</td></tr><tr><td>2</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr><tr><td>4</td><td>65M</td><td>98.4</td><td>96.2</td><td>94.9</td><td>100</td><td>82.4</td><td>88.2</td></tr></table>",
+        "bbox": [
+            367,
+            277,
+            633,
+            335
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/f061fbfa1ae90ca4196cf7add05b0aa11c15dc6dfc79c2924f6e7a47949558fb.jpg",
+        "table_caption": [
+            "Table 5. Cascade stages."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>N_infer</td><td>Param.</td><td>NC</td><td>DAC</td><td>TTC</td><td>Comf.</td><td>EP</td><td>PDMS</td></tr><tr><td>10</td><td>60M</td><td>97.9</td><td>93.5</td><td>93.1</td><td>100</td><td>80.0</td><td>84.9</td></tr><tr><td>20</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr><tr><td>40</td><td>60M</td><td>98.5</td><td>96.2</td><td>94.8</td><td>100</td><td>82.5</td><td>88.2</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 6. Number of sampled noises  ${N}_{\\text{infer }}$  .",
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+    {
+        "type": "text",
+        "text": "merged LiDAR point cloud derived from five sensors. Annotations are provided at a frequency of  $2\\mathrm{Hz}$  and include both HD maps and object bounding boxes. The dataset is designed to emphasize challenging driving scenarios involving dynamic changes in driving intentions, while deliberately excluding trivial situations such as stationary scenes or constant-speed driving.",
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+        "type": "text",
+        "text": "NAVSIM benchmarks planning performance using non-reactive simulations and closed-loop metrics for comprehensive evaluation. In this paper, we employ the proposed PDM score (PDMS) [11], which is a weighted combination of several sub-scores: no at-fault collisions (NC), drivable area compliance (DAC), time-to-collision (TTC), comfort (Comf.), and ego progress (EP).",
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+    {
+        "type": "text",
+        "text": "4.2. Implementation Detail",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We adopt the same perception modules and ResNet-34 backbone [13] as Transfuser for fair comparison. In the diffusion decoder layer, we employ spatial cross-attention to only interact with BEV features following Transfuser's BEV-based setting. We only perform agent cross-attention, since the perception module of Transfuser does not include vectorized map construction. We stack 2 cascade diffusion decoder layers and apply truncated diffusion policy with 20 clustered anchors. The training diffusion schedule is truncated by 50/1000 to diffuse the anchors, while during inference, we use only 2 denoising steps and select the top-1 scoring predicted trajectory for evaluation. The training and inference recipe directly follows Transfuser: We use three cropped and downscaled forward-facing camera images, concatenated as a  $1024 \\times 256$  image, and a rasterized BEV LiDAR as input; DiffusionDrive is trained on navtrain split from scratch for 100 epochs with AdamW optimizer on 8 NVIDIA 4090 GPUs with total batch size of 512, setting the learning rate to  $6 \\times 10^{-4}$ . No test-time",
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+    {
+        "type": "text",
+        "text": "augmentation is applied and the final output for evaluation on navtest split is 8-waypoint trajectory over 4 seconds.",
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+    {
+        "type": "text",
+        "text": "4.3. Quantitative Comparison",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Tab. 1 compares DiffusionDrive with state-of-the-art methods on NAVSIM navtest split. With the same ResNet-34 backbone, DiffusionDrive achieves 88.1 PDMS score, demonstrating significant superior performance over the previous learning-based methods. Compared to VADv2, DiffusionDrive surpasses it by 7.2 PDMS while reducing the number of anchors from 8192 to 20, representing a  $400 \\times$  reduction. DiffusionDrive also outperforms Hydra-MDP, which follows VADv2's sampling-from-vocabulary paradigm, with a 5.1 PDMS improvement. Even compared to the Hydra-MDP- $\\mathcal{V}_{8192}$ -W-EP, which is a variant of Hydra-MDP [25] by further training to fit the EP evaluation metric with additional supervision and using weighted confidence post-processing, DiffusionDrive still outperforms it by 3.5 EP and 1.6 overall PDMS, relying solely on a straightforward learning-from-human approach without any post-processing. Compared to the Transfuser baseline, where we only differ in the planning module, DiffusionDrive delivers a notable 4.1 PDMS improvement, outperforming it across all sub-scores.",
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+    {
+        "type": "text",
+        "text": "4.4. Roadmap",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In Tab. 2, converting Transfuser  $\\mathrm{DP}$  using vanilla diffusion policy improves the PDMS score by 0.6 and the mode diversity score  $\\mathcal{D}$  by  $11\\%$ . However, it also significantly increases the overhead of the planning module, requiring  $20\\times$  more denoising steps and  $32\\times$  the step time, resulting in a total  $650\\times$  increase in runtime overhead. With the proposed truncated diffusion policy,  $\\mathrm{Transfuser}_{\\mathrm{TD}}$  reduces the number of denoising steps from 20 to 2 while improving PDMS by 1.1 and mode diver",
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+    {
+        "type": "page_number",
+        "text": "12043",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/fcc3e04c5f71e323a22828beec3a3aea956064444a32df850c3ee01e1054e61d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Input</td><td rowspan=\"2\">Img. Backbone</td><td colspan=\"4\">L2 (m) ↓</td><td colspan=\"4\">Collision Rate (%) ↓</td><td rowspan=\"2\">FPS ↑</td></tr><tr><td>1s</td><td>2s</td><td>3s</td><td>Avg.</td><td>1s</td><td>2s</td><td>3s</td><td>Avg.</td></tr><tr><td>ST-P3 [15]</td><td>Camera</td><td>EffNet-b4 [40]</td><td>1.33</td><td>2.11</td><td>2.90</td><td>2.11</td><td>0.23</td><td>0.62</td><td>1.27</td><td>0.71</td><td>1.6</td></tr><tr><td>UniAD [16]</td><td>Camera</td><td>ResNet-101 [13]</td><td>0.45</td><td>0.70</td><td>1.04</td><td>0.73</td><td>0.62</td><td>0.58</td><td>0.63</td><td>0.61</td><td>1.8</td></tr><tr><td>OccNet [41]</td><td>Camera</td><td>ResNet-50 [13]</td><td>1.29</td><td>2.13</td><td>2.99</td><td>2.14</td><td>0.21</td><td>0.59</td><td>1.37</td><td>0.72</td><td>2.6</td></tr><tr><td>VAD [20]</td><td>Camera</td><td>ResNet-50 [13]</td><td>0.41</td><td>0.70</td><td>1.05</td><td>0.72</td><td>0.07</td><td>0.17</td><td>0.41</td><td>0.22</td><td>4.5</td></tr><tr><td>SparseDrive [39]</td><td>Camera</td><td>ResNet-50 [13]</td><td>0.29</td><td>0.58</td><td>0.96</td><td>0.61</td><td>0.01</td><td>0.05</td><td>0.18</td><td>0.08</td><td>9.0</td></tr><tr><td>DiffusionDrive (Ours)</td><td>Camera</td><td>ResNet-50 [13]</td><td>0.27</td><td>0.54</td><td>0.90</td><td>0.57</td><td>0.03</td><td>0.05</td><td>0.16</td><td>0.08</td><td>8.2</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 7. Comparison on nuScenes dataset with open-loop metrics. FPS is measured on a single NVIDIA 4090 GPU following the recipe of SparseDrive [39]. Metric calculation follows ST-P3 [15].",
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+    {
+        "type": "text",
+        "text": "sity by  $59\\%$ . By further incorporating the proposed diffusion decoder, the final model, DiffusionDrive, reaches 88.1 PDMS and  $74\\%$  mode diversity score  $\\mathcal{D}$ . Compared to the TransfuserDP, DiffusionDrive shows improvements in 3.5 PDMS and  $64\\%$  mode diversity, and a  $10\\times$  reduction in denoising steps, resulting in a  $6\\times$  speedup in FPS. This enables real-time, high-quality, multi-mode planning.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Effect of designs in diffusion decoder. Tab. 3 shows the effectiveness of our design choices in the diffusion decoder. ID-1 is the Transfuser $_{\\text{TD}}$  in the Tab. 2. By comapring ID-6 and ID-1, we can see that the proposed diffusion decoder reduce the  $39\\%$  parameters and significantly improves the planning quality by 2.4 PDMS. ID-2 shows severe performance degeneration due to the lack of rich and hierarchical interaction with the environment. By comparing ID-2 and ID-3, we show that spatial cross-attention is vital for accurate planning. ID-5 shows that the proposed cascade mechanism is effective and can further improve the performance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Denoising step number. Tab. 4 shows that due to a reasonable start point, DiffusionDrive achieves good planning quality even with only 1 step, and further denoising steps offer quality improvement and inference flexibility for complex environments.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Cascade stages. Tab. 5 ablates the impact of cascade stage number. Increasing the stage number can improve the planning quality but saturate at the 4 stages and cost more parameters and inference time at each step.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Number of sampled noises  $N_{\\mathrm{infer}}$ . As stated in Sec. 3.3, DiffusionDrive can generate varied trajectories by simply sampling a variable number of noises from anchored Gaussian distribution. Tab. 6 shows that 10 sampled noises can already achieve a decent planning quality. By sampling more noises, DiffusionDrive can cover potential planning action space and lead to improved planning quality.",
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+    },
+    {
+        "type": "text",
+        "text": "4.6. Qualitative Comparison",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Since the PDMS planning metric calculates based on the top-1 scoring trajectory and our proposed  $\\mathcal{D}$  score evaluates mode diversity, these metrics alone cannot fully capture the",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "quality of diverse trajectories. To further validate the quality of multi-mode trajectories, we visualize the planning results of Transfuser,  $\\mathrm{Transfuser}_{\\mathrm{DP}}$  and DiffusionDrive on challenging scenarios of NAVSIM navtest split in Fig. 2. The results indicate that the multi-mode trajectories generated by DiffusionDrive are not only diverse but also of high quality. In Fig. 2a, the top-1 scoring trajectory generated by DiffusionDrive closely resembles the ground-truth trajectory, while the highlighted top-10 scoring trajectory surprisingly tries to perform high-quality lane changing. In Fig. 2b, the highlighted top-10 scoring trajectory also performs a lane change, and a neighboring low-scoring trajectory further interacts with surrounding agents to effectively avoid collisions.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.7. Quantitative Comparison on nuScenes dataset",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The nuScenes dataset is previously popular benchmark for end-to-end planning. Since the major scenarios of nuScenes are simple and trivial situations, we only perform comparison in Tab. 7. We implement DiffusionDrive on top of SparseDrive [39] following its training and inference recipe using open-loop metrics proposed in ST-P3 [15]. We stack 2 cascade diffusion decoder layers and apply the truncated diffusion policy with 18 clustered anchors.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As shown in Tab. 7, DiffusionDrive reduces the average L2 error of SparseDrive by  $0.04\\mathrm{m}$ , achieving the lowest L2 error and average collision rate. While DiffusionDrive is also efficient and runs  $1.8\\times$  faster than VAD with  $20.8\\%$  lower L2 error and  $63.6\\%$  lower collision rate.",
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+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a novel generative driving decision-making model, DiffusionDrive, for end-to-end autonomous driving by incorporating the proposed truncated diffusion policy and efficient cascade diffusion decoder. DiffusionDrive can denoise a variable number of samples from an anchored Gaussian distribution to generate diverse planning trajectories at real-time speeds. Comprehensive experiments and qualitative comparisons validate the superiority of DiffusionDrive in planning quality, running efficiency, and mode diversity.",
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+    {
+        "type": "page_number",
+        "text": "12044",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
+            91,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work was partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 62276108. We would like to acknowledge Tianheng Cheng for helpful feedback on the draft.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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2025/DiffusionDrive_ Truncated Diffusion Model for End-to-End Autonomous Driving/186eb20a-812b-4b73-a9f1-a45f01468323_origin.pdf

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2025/DiffusionDrive_ Truncated Diffusion Model for End-to-End Autonomous Driving/full.md

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+# DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving
+
+Bencheng Liao $^{1,2,\diamond}$  Shaoyu Chen $^{2,3}$  Haoran Yin $^{3}$  Bo Jiang $^{2,\diamond}$  Cheng Wang $^{1,2,\diamond}$  Sixu Yan $^{2}$  Xinbang Zhang $^{3}$  Xiangyu Li $^{3}$  Ying Zhang $^{3}$  Qian Zhang $^{3}$  Xinggang Wang $^{2}$ $^{1}$  Institute of Artificial Intelligence, Huazhong University of Science & Technology  
+ $^{2}$  School of EIC, Huazhong University of Science & Technology  
+ $^{3}$  Horizon Robotics  
+Code & Model & Demo: hustvl/DiffusionDrive
+
+# Abstract
+
+Recently, the diffusion model has emerged as a powerful generative technique for robotic policy learning, capable of modeling multi-mode action distributions. Leveraging its capability for end-to-end autonomous driving is a promising direction. However, the numerous denoising steps in the robotic diffusion policy and the more dynamic, open-world nature of traffic scenes pose substantial challenges for generating diverse driving actions at a real-time speed. To address these challenges, we propose a novel truncated diffusion policy that incorporates prior multi-mode anchors and truncates the diffusion schedule, enabling the model to learn denoising from anchored Gaussian distribution to the multi-mode driving action distribution. Additionally, we design an efficient cascade diffusion decoder for enhanced interaction with conditional scene context. The proposed model, DiffusionDrive, demonstrates  $10 \times$  reduction in denoising steps compared to vanilla diffusion policy, delivering superior diversity and quality in just 2 steps. On the planning-oriented NAVSIM dataset, with aligned ResNet-34 backbone, DiffusionDrive achieves 88.1 PDMS without bells and whistles, setting a new record, while running at a real-time speed of 45 FPS on an NVIDIA 4090. Qualitative results on challenging scenarios further confirm that DiffusionDrive can robustly generate diverse plausible driving actions.
+
+# 1. Introduction
+
+End-to-end autonomous driving has gained significant attention in recent years due to advancements in perception models (detection [5, 17, 24, 42], tracking [54-56], online mapping [27, 28, 32], etc.), which directly learns the driving policy from the raw sensor inputs. This data-driven ap
+
+![](images/99b5d280af68662c38a293d2104fb29b5b421a613a42c76a54486e13cbbd3e04.jpg)  
+Figure 1. The comparison of different end-to-end paradigms. (a) Single mode regression [8, 16, 20]. (b) Sampling from vocabulary [4, 25]. (c) Vanilla diffusion policy [7, 19]. (d) The proposed truncated diffusion policy.
+
+proach offers a scalable and robust alternative to traditional rule-based motion planning, which often struggles to generalize to complex real-world driving settings.
+
+To effectively learn from data, mainstream end-to-end planners (e.g., Transfuser [8], UniAD [16], VAD [20]) typically regress a single-mode trajectory from an ego-query as shown in Fig. 1a. However, this paradigm does not account for the inherent uncertainty and multi-mode nature of driving behaviors. Recently, VADv2 [20] introduces a large fixed vocabulary of anchor trajectories (4096 anchors) to discretize the continuous action space and capture a broader range of driving behaviors, and then samples from these anchors based on predicted scores as shown in Fig. 1b. However, this large fixed-vocabulary paradigm is fundamentally constrained by the number and quality of anchor trajectories, often failing in out-of-vocabulary scenarios. Furthermore, managing a large number of anchors presents significant computational challenges for real-time applications. Rather than discretizing the action space, diffusion model [7] has proven to be a powerful genera
+
+tive decision-making policy in the robotics domain, which can directly sample multi-mode physically plausible actions from a Gaussian distribution via iterative denoising process.
+
+This inspires us to replicate the success of the diffusion model in the robotics domain to end-to-end autonomous driving. We apply the vanilla robotic diffusion policy to the well-known single-mode-regression method, Transfuser [8], by proposing a variant,  $\text{Transfuser}_{\text{DP}}$ , which replaces the deterministic MLP regression head with a conditional diffusion model [34]. Though  $\text{Transfuser}_{\text{DP}}$  improves planning performance, two major issues arise: 1) The numerous 20 denoising steps in the vanilla DDIM diffusion policy introduce heavy computational consumption during inference as shown in Tab. 2, hindering the real-time application for autonomous driving. 2) The trajectories sampled from different Gaussian noises severely overlap with each other, as illustrated in Fig. 2. This underscores the non-trivial challenge of taming the diffusion models for the dynamic and open-world traffic scenes.
+
+Unlike the vanilla diffusion policy, which samples actions from a random Gaussian noise conditioned on scene context, human drivers adhere to established driving patterns that they dynamically adjust in response to real-time traffic conditions. This insight motivates us to embed these prior driving patterns into the diffusion policy by partitioning the Gaussian distribution into multiple sub-Gaussian distributions centered around prior anchors, referred to as anchored Gaussian distribution. It is implemented by truncating the diffusion schedule to introduce a small portion of Gaussian noise around the prior anchors as shown in Fig. 3. Thanks to the multi-mode distributional expressivity of the diffusion model, the proposed truncated diffusion policy effectively covers the potential action space without requiring a large set of fixed anchors, as VADv2 does. With more reasonable initial noise samples from the anchored Gaussian distribution, we can truncate the denoising process, reducing the required steps from 20 to just 2—a substantial speedup that satisfies the real-time requirements of autonomous driving.
+
+To enhance the interaction with conditional scene context, we propose an efficient transformer-based diffusion decoder that interacts not only with structured queries from the perception module but also with Bird's Eye View (BEV) and perspective view (PV) features through a sparse deformable attention mechanism [3, 62]. Additionally, we introduce a cascade mechanism to iteratively refine the trajectory reconstruction within the diffusion decoder at each denoising step.
+
+With these innovations, we present DiffusionDrive, a diffusion model for real-time end-to-end autonomous driving. We benchmark our method on the planning-oriented NAVSIM dataset [11] using non-reactive simulation and closed-loop evaluations. Without bells and whis
+
+tles, DiffusionDrive achieves 88.1 PDMS on NAVSIM navtest split with the aligned ResNet-34 backbone, significantly outperforming previous state-of-the-art methods. Even compared to the NAVSIM challenge-winning solution Hydra-MDP- $\nu_{8192}$ -W-EP [25], which follows VADv2 with 8192 anchor trajectories and further incorporates post-processing and additional supervision, DiffusionDrive still outperforms it by 1.6 PDMS through directly learning from human demonstrations and inferring without post-processing, while running at real-time speed of 45 FPS on an NVIDIA 4090. We further validate the superiority of DiffusionDrive on popular nuScenes dataset [2] with open-loop evaluations, DiffusionDrive runs  $1.8 \times$  faster than VAD and outperforms it [20] by  $20.8\%$  lower L2 error and  $63.6\%$  lower collision rate with the same ResNet-50 backbone, demonstrating state-of-the-art planning performance.
+
+Our contributions can be summarized as follows:
+
+- We firstly introduce the diffusion model to the field of end-to-end autonomous driving and propose a novel truncated diffusion policy to address the issues of mode collapse and heavy computational overhead found in direct adaptation of vanilla diffusion policy to the traffic scene.  
+- We design an efficient transformer-based diffusion decoder that interacts with the conditional information in a cascaded manner for better trajectory reconstruction.  
+- Without bells and whistles, DiffusionDrive significantly outperforms previous state-of-the-art methods, achieving a record-breaking 88.1 PDMS on the NAVSIM navtest split with the same backbone, while maintaining real-time performance at 45 FPS on an NVIDIA 4090.  
+- We qualitatively demonstrate that DiffusionDrive can generate more diverse and plausible trajectories, exhibiting high-quality multi-mode driving actions in various challenging scenarios.
+
+# 2. Related Work
+
+End-to-end autonomous driving. UniAD [16], as a pioneering work, demonstrates the potential of end-to-end autonomous driving by integrating multiple perception tasks to enhance planning performance. VAD [20] further explores the use of compact vectorized scene representations to improve efficiency. Subsequently, a series of works [6, 8, 12, 23, 26, 43, 45, 58] have adopted the single-trajectory planning paradigm to enhance planning performance further. More recently, VADv2 [4] shifts the paradigm towards multi-mode planning by scoring and sampling from a large fixed vocabulary of anchor trajectories. Hydra-MDP [25] improves the scoring mechanism of VADv2 by introducing extra supervision from a rule-based scorer. SparseDrive [39] explores an alternative BEV-free solution. Unlike existing multi-mode planning approaches, we propose a novel paradigm that leverages powerful generative diffusion models for end-to-end autonomous driving.
+
+![](images/eae6cbced2a079f01e0437de2d3082d21ee7f04b1c9e9400b61c9f8776e04382.jpg)  
+(b) Top-1's turning left and diverse top-10's lane changing.  
+Figure 2. Qualitative comparison of Transfuser, TransfuserDP and DiffusionDrive on challenging scenes of NAVSIM navtest split. With the same inputs from front cameras and LiDAR, DiffusionDrive achieves the highest planning quality of top-1 scoring trajectory as illustrated in Tab. 2. We render the highlighted diverse trajectories predicted by DiffusionDrive in the front view. (a) and (b) shows that the top-1 scoring trajectory of DiffusionDrive closely matches the ground truth for both going straight and turning left. Additionally, DiffusionDrive's top-10 scoring trajectory demonstrates high-quality lane changing—an ability not observed in multi-mode TransfuserDP and impossible for Transfuser.
+
+Diffusion model for traffic simulation. Driving diffusion policy has been explored in the traffic simulation by leveraging only abstract perception groundtruth [9, 18, 21, 44]. MotionDiffuser [21] and CTG [60] are pioneering applications of diffusion models for multi-agent motion prediction, using a conditional diffusion model to sample target trajectories from Gaussian noise.  $\mathrm{CTG + + }$  [59] further incorporates a large language model (LLM) for language-driven guidance, improving usability and enabling realistic traffic simulations. Diffusion-ES [48] replaces reward-gradient-guided denoising with evolutionary search. Moving beyond diffusion models limited to traffic simulation with perception groundtruth, our approach unlocks the potential of dif
+
+fusion models for real-time, end-to-end autonomous driving through our proposed truncated diffusion policy and efficient diffusion decoder.
+
+Diffusion model for robotic policy learning. Diffusion policy [7] demonstrates the great potential in robotic policy learning, effectively capturing multi-mode action distributions and high-dimensional action spaces. Diffuser [19] proposes an unconditional diffusion model for trajectory sampling, incorporating techniques such as classifier-free guidance and image inpainting to achieve guided sampling. Subsequently, numerous works have applied diffusion models to various robotic tasks, including stationary manipulation [1, 53], mobile manipulation [47], autonomous nav
+
+Diffusion step:  $q(\tau^i |\tau^{i - 1}),i\in [1,T]$
+
+![](images/8cfefc6af824cac1c473f324a6793a77eea43f897f66e0c85228a8fc8fda716a.jpg)
+
+Denoising step:  $p_{\theta}\big(\tau^i |\tau^{i - 1},z\big),i\in [1,T]$
+
+# Vanilla Diffusion Policy vs. Truncated Diffusion Policy (ours)
+
+Diffusion step:  $q(\tau^i |\tau^{i - 1}),i\in [1,T_{\mathrm{trunc}}]$
+
+![](images/908ca90015f3cdef9e8a7a268d4d0e4dffad49b35c5355a18d9a23521945317e.jpg)  
+Adding noise to the anchors with truncated diffusion schedule.
+
+Denosing from anchored Gaussian distribution with fewer steps.
+
+![](images/90462a069ee2704c6c9619343f1e37dcc31b96ef9d735cc9113ee30ae82e944a.jpg)  
+Denoising step:  $p_{\theta}(\tau^i |\tau^{i - 1},z),i\in [1,T_{\mathrm{trunc}}]$  
+Figure 3. Illustration of truncated diffusion policy by comparing with vanilla diffusion policy. We truncate the diffusion process and only add a small portion of Gaussian noise to diffuse the anchor trajectories. Then, we train the diffusion model to reconstruct the ground-truth trajectory from the anchored Gaussian distribution with conditional scene context. During the inference, we also truncate the denoising process by starting from the better samples in the anchored Gaussian distribution than the pure Gaussian noise.
+
+igation [37, 51], quadruped locomotion [38], and dexterous manipulation [46]. However, directly applying vanilla diffusion policy to end-to-end autonomous driving poses unique challenges, as it requires real-time efficiency and the generation of plausible multi-mode trajectories in dynamic and open-world traffic scenes. In this work, we propose a novel truncated diffusion policy to address these challenges, introducing concepts that have not yet been explored in the robotics field.
+
+Diffusion model for image generation. Diffusion models have been extensively adopted for image generation tasks [33, 36, 49, 50, 61]. DDIM [35] enhances DDPM [14] by enabling efficient sampling with significantly fewer steps based on non-Markovian diffusion processes. Flow matching [30, 31] further optimizes the generative process by directly modeling continuous probability flows. TDPM [57] proposes truncated denoising, which initiates the generation process from an implicit intermediate distribution to accelerate sampling. In contrast to these approaches, our method introduces an explicit driving prior within the diffusion policy, effectively guiding the diffusion process toward more accurate and efficient generation tailored specifically for end-to-end autonomous driving.
+
+# 3. Method
+
+# 3.1. Preliminary
+
+Task formulation. End-to-end autonomous driving takes raw sensor data as input and predicts the future trajectory of the ego-vehicle. The trajectory is represented as a sequence of waypoints  $\tau = \{(x_{t},y_{t})\}_{t = 1}^{T_{f}}$ , where  $T_{f}$  denotes the planning horizon, and  $(x_{t},y_{t})$  is the location of each waypoint at time  $t$  in the current ego-vehicle coordinate system.
+
+Conditional diffusion model. The conditional diffusion model poses a forward diffusion process as gradually adding noise to the data sample, which can be defined as:
+
+$$
+q \left(\tau^ {i} \mid \tau^ {0}\right) = \mathcal {N} \left(\tau^ {i}; \sqrt {\bar {\alpha} ^ {i}} \boldsymbol {\tau} ^ {0}, \left(1 - \bar {\alpha} ^ {i}\right) \mathbf {I}\right), \tag {1}
+$$
+
+where  $\tau^0$  is the clean data sample, and  $\tau^i$  is the data sample with noise at time  $i$  (Note: we use superscript  $i$  to denote diffusion timestep). The constant  $\bar{\alpha}^i = \prod_{s=1}^i \alpha^s = \prod_{s=1}^i (1 - \beta^s)$  and  $\beta^s$  is the noise schedule. We train the reverse process model  $f_\theta(\tau^i, z, i)$  to predict  $\tau^0$  from  $\tau^i$  with the guidance of conditional information  $z$ , where  $\theta$  is the trainable model parameter. During inference, the trained diffusion model  $f_\theta$  progressively refines from the random
+
+![](images/39188c906af22969f52df93d3eccb03e17c013632528cf929e933086a49a30e7.jpg)  
+Figure 4. Overall architecture of DiffusionDrive. (a) DiffusionDrive can integrate various existing perception modules and sensor inputs. (b) The designed diffusion decoder takes the sampled noisy trajectories from anchored Gaussian distribution as input and progressively denoises them with enhanced interactions with the conditional scene context in a cascade manner to generate the final predictions.
+
+![](images/3501d4a7121777ea39ebdd62ca4e2b3efafa5c0f6dd4428085611e154596d12e.jpg)
+
+noise  $\tau^T$  sampled in Gaussian distribution to the predicted clean data sample  $\tau^0$  with the guidance of conditional information  $z$ , which is defined as:
+
+$$
+p _ {\theta} \left(\boldsymbol {\tau} ^ {0} \mid z\right) = \int p \left(\boldsymbol {\tau} ^ {T}\right) \prod_ {i = 1} ^ {T} p _ {\theta} \left(\boldsymbol {\tau} ^ {i - 1} \mid \boldsymbol {\tau} ^ {i}, z\right) d \boldsymbol {\tau} ^ {1: T}. \tag {2}
+$$
+
+# 3.2. Investigation
+
+Turn Transfuser [8] into conditional diffusion model. We begin from the representative deterministic end-to-end planner Transfuser [8] and turn it into a generative model  $\mathrm{Transfuser}_{\mathrm{DP}}$  by simply replacing the regression MLP layers with the conditional diffusion model UNet following vanilla diffusion policy [7]. During the evaluation, we sample a random noise and progressively refine it with 20 steps. Tab. 2 shows that  $\mathrm{Transfuser}_{\mathrm{DP}}$  achieves better planning quality than deterministic Transfuser.
+
+Mode collapse. To further investigate the multi-mode property of the vanilla diffusion policy in driving, we sampled 20 random noises from Gaussian distribution and denoised them using 20 steps. As shown in Fig. 2, the different random noises converge to similar trajectories after the denoising process. To quantitatively analyze the phenomenon of mode collapse, we define a mode diversity score  $\mathcal{D}$  based on the mean Intersection over Union (mIoU) between each denoised trajectory and the union of all denoised trajectories:
+
+$$
+\mathcal {D} = 1 - \frac {1}{N} \sum_ {i = 1} ^ {N} \frac {\operatorname {A r e a} \left(\tau_ {i} \cap \bigcup_ {j = 1} ^ {N} \tau_ {j}\right)}{\operatorname {A r e a} \left(\tau_ {i} \cup \bigcup_ {j = 1} ^ {N} \tau_ {j}\right)}, \tag {3}
+$$
+
+where  $\tau_{i}$  represents the  $i$ -th denoised trajectory,  $N$  is the total number of sampled trajectories and  $\bigcup_{j=1}^{N} \tau_{j}$  is the union of all denoised trajectories. A higher mIoU indicates less diversity of the denoised trajectories. The quantitative mode diversity results in Tab. 2 further validate the observations presented in Fig. 2.
+
+Heavy denoising overhead. The DDIM [35] diffusion policy requires 20 denoising steps to transform random noise
+
+into a feasible trajectory, which introduces significant computational overhead, reducing the FPS from 60 to 7, as shown in Tab. 2, and making it impractical for real-time online driving applications.
+
+# 3.3. Truncated Diffusion
+
+Human driving follows fixed patterns, unlike the random noise denoising in vanilla diffusion policy. Motivated by this, we propose a truncated diffusion policy that begins the denoising process from an anchored Gaussian distribution instead of a standard Gaussian distribution. To enable the model to learn to denoise from the anchored Gaussian distribution to the desired driving policy, we further truncate the diffusion schedule during training, adding only a small amount of Gaussian noise to the anchors.
+
+Training. We first construct the diffusion process by adding Gaussian noise to anchors  $\{\mathbf{a}_k\}_{k=1}^{N_{\text{anchor}}}$  clustered by K-Means on the training set, where  $\mathbf{a}_k = \{(x_t, y_t)\}_{t=1}^{T_f}$ . We truncate the diffusion noise schedule to diffuse the anchors to the anchored Gaussian distribution:
+
+$$
+\tau_ {k} ^ {i} = \sqrt {\bar {\alpha} ^ {i}} \mathbf {a} _ {k} + \sqrt {1 - \bar {\alpha} ^ {i}} \boldsymbol {\epsilon}, \quad \boldsymbol {\epsilon} \sim \mathcal {N} (0, \mathbf {I}), \qquad (4)
+$$
+
+where  $i \in [1, T_{\mathrm{trunc}}]$  and  $T_{\mathrm{trunc}} \ll T$  is the truncated diffusion steps.
+
+During training, the diffusion decoder  $f_{\theta}$  takes as input  $N_{\mathrm{anchor}}$  noisy trajectories  $\{\tau_k^i\}_{k=1}^{N_{\mathrm{anchor}}}$  and predicts classification scores  $\{\hat{s}_k\}_{k=1}^{N_{\mathrm{anchor}}}$  and denoised trajectories  $\{\hat{\tau}_k\}_{k=1}^{N_{\mathrm{anchor}}}$ :
+
+$$
+\left\{\hat {s} _ {k}, \hat {\tau} _ {k} \right\} _ {k = 1} ^ {N _ {\text {a n c h o r}}} = f _ {\theta} \left(\left\{\tau_ {k} ^ {i} \right\} _ {k = 1} ^ {N _ {\text {a n c h o r}}}, z\right), \tag {5}
+$$
+
+where  $z$  represents the conditional information. We assign the noisy trajectory around the closest anchor to the ground truth trajectory  $\tau_{\mathrm{gt}}$  as positive sample  $(y_k = 1)$  and others as negative samples  $(y_k = 0)$ . The training objective combines trajectory reconstruction and classification:
+
+$$
+\mathcal {L} = \sum_ {k = 1} ^ {N _ {\text {a n c h o r}}} \left[ y _ {k} \mathcal {L} _ {\text {r e c}} \left(\hat {\tau} _ {k}, \tau_ {\mathrm {g t}}\right) + \lambda \mathrm {B C E} \left(\hat {s} _ {k}, y _ {k}\right) \right], \tag {6}
+$$
+
+<table><tr><td>Method</td><td>Input</td><td>Img. Backbone</td><td>Anchor</td><td>NC↑</td><td>DAC ↑</td><td>TTC ↑</td><td>Comf. ↑</td><td>EP ↑</td><td>PDMS ↑</td></tr><tr><td>UniAD [16]</td><td>Camera</td><td>ResNet-34 [13]</td><td>0</td><td>97.8</td><td>91.9</td><td>92.9</td><td>100</td><td>78.8</td><td>83.4</td></tr><tr><td>PARA-Drive [45]</td><td>Camera</td><td>ResNet-34 [13]</td><td>0</td><td>97.9</td><td>92.4</td><td>93.0</td><td>99.8</td><td>79.3</td><td>84.0</td></tr><tr><td>LTF [8]</td><td>Camera</td><td>ResNet-34 [13]</td><td>0</td><td>97.4</td><td>92.8</td><td>92.4</td><td>100</td><td>79.0</td><td>83.8</td></tr><tr><td>Transfuser [8]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>0</td><td>97.7</td><td>92.8</td><td>92.8</td><td>100</td><td>79.2</td><td>84.0</td></tr><tr><td>DRAMA [52]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>0</td><td>98.0</td><td>93.1</td><td>94.8</td><td>100</td><td>80.1</td><td>85.5</td></tr><tr><td>VADv2- \( \mathcal{V}_{8192} \) [4]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>8192</td><td>97.2</td><td>89.1</td><td>91.6</td><td>100</td><td>76.0</td><td>80.9</td></tr><tr><td>Hydra-MDP- \( \mathcal{V}_{8192} \) [25]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>8192</td><td>97.9</td><td>91.7</td><td>92.9</td><td>100</td><td>77.6</td><td>83.0</td></tr><tr><td>Hydra-MDP- \( \mathcal{V}_{8192} \)-W-EP [25]</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>8192</td><td>98.3</td><td>96.0</td><td>94.6</td><td>100</td><td>78.7</td><td>86.5</td></tr><tr><td>DiffusionDrive (Ours)</td><td>C &amp; L</td><td>ResNet-34 [13]</td><td>20</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr></table>
+
+Table 1. Comparison on planning-oriented NAVSIM navtest split with closed-loop metrics. “C & L” denotes the use of both camera and LiDAR as sensor inputs. “ $\mathcal{V}_{8192}$ ” denotes 8192 anchors. “Hydra-MDP- $\mathcal{V}_{8192}$ -W-EP” is a variant of Hydra-MDP [25], which is further trained to fit the EP evaluation metric with additional supervision from the rule-based evaluator and uses weighted confidence post-processing. DiffusionDrive simply learns from human demonstrations and infers without post-processing. The best and the second best results are denoted by bold and underline.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">NC↑</td><td rowspan="2">DAC↑</td><td rowspan="2">TTC↑</td><td rowspan="2">Comf.↑</td><td rowspan="2">EP↑</td><td rowspan="2">PDMS↑</td><td rowspan="2">Arch.</td><td colspan="3">Plan Module Time</td><td rowspan="2">Total ↓</td><td rowspan="2">D↑</td><td rowspan="2">Para.↓</td><td rowspan="2">FPS↑</td></tr><tr><td>Step Time↓</td><td>Steps ↓</td><td></td></tr><tr><td>Transfuser</td><td>97.7</td><td>92.8</td><td>92.8</td><td>100</td><td>79.2</td><td>84.0</td><td>MLP</td><td>0.2ms</td><td>1</td><td>0.2ms</td><td>0%</td><td>56M</td><td>60</td><td></td></tr><tr><td>TransfuserDP</td><td>97.5</td><td>93.7</td><td>92.7</td><td>100</td><td>79.4</td><td>84.6+0.6</td><td>UNet</td><td>6.5ms</td><td>20</td><td>130.0ms</td><td>11%</td><td>101M</td><td>7</td><td></td></tr><tr><td>TransfuserTD</td><td>97.9</td><td>94.2</td><td>93.9</td><td>100</td><td>80.2</td><td>85.7+1.7</td><td>UNet</td><td>6.9ms</td><td>2</td><td>13.8ms</td><td>70%</td><td>102M</td><td>27</td><td></td></tr><tr><td>DiffusionDrive</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1+4.1</td><td>Dec.</td><td>3.8ms</td><td>2</td><td>7.6ms</td><td>74%</td><td>60M</td><td>45</td><td></td></tr></table>
+
+Table 2. Roadmap from Transfuser to DiffusionDrive on NAVSIM navtest split. "TransfuserDP" denotes Transfuser with vanilla DDIM diffusion policy [7]. "TransfuserTD" denotes Transfuser with truncated diffusion policy. "Step Time" denotes the runtime of each denoising step. "FPS" and runtime are measured on an NVIDIA 4090 GPU. "D" denotes the mode diversity score defined in Eq. (3).
+
+where  $\lambda$  balances the simple L1 reconstruction loss  $\mathcal{L}_{\mathrm{rec}}$  and binary cross-entropy (BCE) classification loss.
+
+Inference. We use a truncated denoising process that starts with noisy trajectories sampled from the anchored Gaussian distribution and progressively denoises them to final predictions. At each denoising timestep, the estimated trajectories from the previous step are passed to the diffusion decoder  $f_{\theta}$ , which predicts classification scores  $\{\hat{s}_k\}_{k=1}^{N_{\mathrm{infer}}}$  and coordinates  $\{\hat{\tau}_k\}_{k=1}^{N_{\mathrm{infer}}}$ . After obtaining the current timestep's predictions, we apply the DDIM [35] update rule to sample trajectories for the next timestep.
+
+Inference flexibility. A key advantage of our approach lies in its inference flexibility. While the model is trained with  $N_{\text{anchor}}$  trajectories, the inference process can accommodate an arbitrary number of trajectory samples  $N_{\text{infer}}$ , where  $N_{\text{infer}}$  can be dynamically adjusted based on computational resources or application requirements.
+
+# 3.4. Architecture
+
+The overall architecture of our proposed method, DiffusionDrive, is illustrated in Fig. 4. DiffusionDrive can integrate various existing perception modules used in previous end-to-end planners [8, 16, 20, 39] and take different sensor inputs. The designed diffusion decoder is tailored for the complex and challenging driving application, which has enhanced interactions with the conditional scene context.
+
+Diffusion decoder. Given the set of sampled noisy trajectories
+
+ries  $\{\hat{\tau}_k\}_{k=1}^{N_{\mathrm{infer}}}$  from the anchored Gaussian distribution, we begin by applying deformable spatial cross-attention [29, 42, 62] to interact with Bird's Eye View (BEV) or Perspective View (PV) features based on the trajectory coordinates. Subsequently, cross-attention is performed between the trajectory features and the agent/map queries derived from the perception module, followed by a feed-forward network (FFN). To encode the diffusion timestep information, we utilize a Timestep Modulation layer, which is followed by a Multi-Layer Perceptron (MLP) that predicts the confidence score and the offset relative to the initial noisy trajectory coordinates. The output from this diffusion decoder layer serves as the input for the subsequent cascade diffusion decoder layer. DiffusionDrive further reuses the cascade diffusion decoder to iteratively denoise the trajectory during inference, with parameters shared across the different denoising timesteps. The final trajectory with the highest confidence score is selected as the output.
+
+# 4. Experiment
+
+# 4.1. Dataset
+
+NAVSIM. The NAVSIM dataset [11] is a real-world planning-oriented dataset builds upon OpenScene [10], a compact redistribution of nuPlan [22], the largest publicly available annotated driving dataset. NAVSIM leverages eight cameras to achieve a full  $360^{\circ}$  FOV, along with a
+
+<table><tr><td rowspan="2">ID</td><td rowspan="2">UNet Decoder</td><td rowspan="2">Ego Query Interaction</td><td rowspan="2">Spatial Cross-attn</td><td rowspan="2">Agent/Map Cross-attn</td><td rowspan="2">Cascade Decoder</td><td rowspan="2">Param.↓</td><td rowspan="2">NC↑</td><td rowspan="2">DAC↑</td><td colspan="4">Planning Metric</td><td rowspan="2">PDMS↑</td></tr><tr><td>TTC↑</td><td>Comf.↑</td><td>EP↑</td><td></td></tr><tr><td>1</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>102M</td><td>97.9</td><td>94.2</td><td>93.9</td><td>100</td><td>80.2</td><td></td><td>85.7</td></tr><tr><td>2</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>57M</td><td>88.7</td><td>83.2</td><td>80.0</td><td>84.8</td><td>43.3</td><td></td><td>55.1</td></tr><tr><td>3</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>58M</td><td>98.2</td><td>95.4</td><td>94.4</td><td>100</td><td>81.3</td><td></td><td>87.1</td></tr><tr><td>4</td><td>X</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>58M</td><td>97.9</td><td>93.5</td><td>93.8</td><td>100</td><td>79.8</td><td></td><td>85.1</td></tr><tr><td>5</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>59M</td><td>98.0</td><td>95.8</td><td>94.4</td><td>100</td><td>81.7</td><td></td><td>87.4</td></tr><tr><td>6</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td></td><td>88.1</td></tr></table>
+
+Table 3. Ablation for design choices. "Cascade Decoder" indicates that we stack 2 cascade diffusion decoder layers. ID-1 refers to TransfuserTD in Tab. 2, utilizing conditional UNet and interaction with the ego-query, which Transfuser uses to directly regress the single-mode trajectory.  
+
+<table><tr><td>Steps</td><td>Param.</td><td>NC</td><td>DAC</td><td>TTC</td><td>Comf.</td><td>EP</td><td>PDMS</td></tr><tr><td>1</td><td>60M</td><td>98.3</td><td>96.0</td><td>94.7</td><td>100</td><td>82.1</td><td>87.9</td></tr><tr><td>2</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr><tr><td>3</td><td>60M</td><td>98.2</td><td>96.3</td><td>94.7</td><td>100</td><td>92.2</td><td>88.1</td></tr></table>
+
+Table 4. Denoising step number.  
+
+<table><tr><td>Stages</td><td>Param.</td><td>NC</td><td>DAC</td><td>TTC</td><td>Comf.</td><td>EP</td><td>PDMS</td></tr><tr><td>1</td><td>59M</td><td>98.0</td><td>95.8</td><td>94.4</td><td>100</td><td>81.7</td><td>87.4</td></tr><tr><td>2</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr><tr><td>4</td><td>65M</td><td>98.4</td><td>96.2</td><td>94.9</td><td>100</td><td>82.4</td><td>88.2</td></tr></table>
+
+Table 5. Cascade stages.  
+
+<table><tr><td>N_infer</td><td>Param.</td><td>NC</td><td>DAC</td><td>TTC</td><td>Comf.</td><td>EP</td><td>PDMS</td></tr><tr><td>10</td><td>60M</td><td>97.9</td><td>93.5</td><td>93.1</td><td>100</td><td>80.0</td><td>84.9</td></tr><tr><td>20</td><td>60M</td><td>98.2</td><td>96.2</td><td>94.7</td><td>100</td><td>82.2</td><td>88.1</td></tr><tr><td>40</td><td>60M</td><td>98.5</td><td>96.2</td><td>94.8</td><td>100</td><td>82.5</td><td>88.2</td></tr></table>
+
+Table 6. Number of sampled noises  ${N}_{\text{infer }}$  .
+
+merged LiDAR point cloud derived from five sensors. Annotations are provided at a frequency of  $2\mathrm{Hz}$  and include both HD maps and object bounding boxes. The dataset is designed to emphasize challenging driving scenarios involving dynamic changes in driving intentions, while deliberately excluding trivial situations such as stationary scenes or constant-speed driving.
+
+NAVSIM benchmarks planning performance using non-reactive simulations and closed-loop metrics for comprehensive evaluation. In this paper, we employ the proposed PDM score (PDMS) [11], which is a weighted combination of several sub-scores: no at-fault collisions (NC), drivable area compliance (DAC), time-to-collision (TTC), comfort (Comf.), and ego progress (EP).
+
+# 4.2. Implementation Detail
+
+We adopt the same perception modules and ResNet-34 backbone [13] as Transfuser for fair comparison. In the diffusion decoder layer, we employ spatial cross-attention to only interact with BEV features following Transfuser's BEV-based setting. We only perform agent cross-attention, since the perception module of Transfuser does not include vectorized map construction. We stack 2 cascade diffusion decoder layers and apply truncated diffusion policy with 20 clustered anchors. The training diffusion schedule is truncated by 50/1000 to diffuse the anchors, while during inference, we use only 2 denoising steps and select the top-1 scoring predicted trajectory for evaluation. The training and inference recipe directly follows Transfuser: We use three cropped and downscaled forward-facing camera images, concatenated as a  $1024 \times 256$  image, and a rasterized BEV LiDAR as input; DiffusionDrive is trained on navtrain split from scratch for 100 epochs with AdamW optimizer on 8 NVIDIA 4090 GPUs with total batch size of 512, setting the learning rate to  $6 \times 10^{-4}$ . No test-time
+
+augmentation is applied and the final output for evaluation on navtest split is 8-waypoint trajectory over 4 seconds.
+
+# 4.3. Quantitative Comparison
+
+Tab. 1 compares DiffusionDrive with state-of-the-art methods on NAVSIM navtest split. With the same ResNet-34 backbone, DiffusionDrive achieves 88.1 PDMS score, demonstrating significant superior performance over the previous learning-based methods. Compared to VADv2, DiffusionDrive surpasses it by 7.2 PDMS while reducing the number of anchors from 8192 to 20, representing a  $400 \times$  reduction. DiffusionDrive also outperforms Hydra-MDP, which follows VADv2's sampling-from-vocabulary paradigm, with a 5.1 PDMS improvement. Even compared to the Hydra-MDP- $\mathcal{V}_{8192}$ -W-EP, which is a variant of Hydra-MDP [25] by further training to fit the EP evaluation metric with additional supervision and using weighted confidence post-processing, DiffusionDrive still outperforms it by 3.5 EP and 1.6 overall PDMS, relying solely on a straightforward learning-from-human approach without any post-processing. Compared to the Transfuser baseline, where we only differ in the planning module, DiffusionDrive delivers a notable 4.1 PDMS improvement, outperforming it across all sub-scores.
+
+# 4.4. Roadmap
+
+In Tab. 2, converting Transfuser  $\mathrm{DP}$  using vanilla diffusion policy improves the PDMS score by 0.6 and the mode diversity score  $\mathcal{D}$  by  $11\%$ . However, it also significantly increases the overhead of the planning module, requiring  $20\times$  more denoising steps and  $32\times$  the step time, resulting in a total  $650\times$  increase in runtime overhead. With the proposed truncated diffusion policy,  $\mathrm{Transfuser}_{\mathrm{TD}}$  reduces the number of denoising steps from 20 to 2 while improving PDMS by 1.1 and mode diver
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Input</td><td rowspan="2">Img. Backbone</td><td colspan="4">L2 (m) ↓</td><td colspan="4">Collision Rate (%) ↓</td><td rowspan="2">FPS ↑</td></tr><tr><td>1s</td><td>2s</td><td>3s</td><td>Avg.</td><td>1s</td><td>2s</td><td>3s</td><td>Avg.</td></tr><tr><td>ST-P3 [15]</td><td>Camera</td><td>EffNet-b4 [40]</td><td>1.33</td><td>2.11</td><td>2.90</td><td>2.11</td><td>0.23</td><td>0.62</td><td>1.27</td><td>0.71</td><td>1.6</td></tr><tr><td>UniAD [16]</td><td>Camera</td><td>ResNet-101 [13]</td><td>0.45</td><td>0.70</td><td>1.04</td><td>0.73</td><td>0.62</td><td>0.58</td><td>0.63</td><td>0.61</td><td>1.8</td></tr><tr><td>OccNet [41]</td><td>Camera</td><td>ResNet-50 [13]</td><td>1.29</td><td>2.13</td><td>2.99</td><td>2.14</td><td>0.21</td><td>0.59</td><td>1.37</td><td>0.72</td><td>2.6</td></tr><tr><td>VAD [20]</td><td>Camera</td><td>ResNet-50 [13]</td><td>0.41</td><td>0.70</td><td>1.05</td><td>0.72</td><td>0.07</td><td>0.17</td><td>0.41</td><td>0.22</td><td>4.5</td></tr><tr><td>SparseDrive [39]</td><td>Camera</td><td>ResNet-50 [13]</td><td>0.29</td><td>0.58</td><td>0.96</td><td>0.61</td><td>0.01</td><td>0.05</td><td>0.18</td><td>0.08</td><td>9.0</td></tr><tr><td>DiffusionDrive (Ours)</td><td>Camera</td><td>ResNet-50 [13]</td><td>0.27</td><td>0.54</td><td>0.90</td><td>0.57</td><td>0.03</td><td>0.05</td><td>0.16</td><td>0.08</td><td>8.2</td></tr></table>
+
+Table 7. Comparison on nuScenes dataset with open-loop metrics. FPS is measured on a single NVIDIA 4090 GPU following the recipe of SparseDrive [39]. Metric calculation follows ST-P3 [15].
+
+sity by  $59\%$ . By further incorporating the proposed diffusion decoder, the final model, DiffusionDrive, reaches 88.1 PDMS and  $74\%$  mode diversity score  $\mathcal{D}$ . Compared to the TransfuserDP, DiffusionDrive shows improvements in 3.5 PDMS and  $64\%$  mode diversity, and a  $10\times$  reduction in denoising steps, resulting in a  $6\times$  speedup in FPS. This enables real-time, high-quality, multi-mode planning.
+
+# 4.5. Ablation Study
+
+Effect of designs in diffusion decoder. Tab. 3 shows the effectiveness of our design choices in the diffusion decoder. ID-1 is the Transfuser $_{\text{TD}}$  in the Tab. 2. By comapring ID-6 and ID-1, we can see that the proposed diffusion decoder reduce the  $39\%$  parameters and significantly improves the planning quality by 2.4 PDMS. ID-2 shows severe performance degeneration due to the lack of rich and hierarchical interaction with the environment. By comparing ID-2 and ID-3, we show that spatial cross-attention is vital for accurate planning. ID-5 shows that the proposed cascade mechanism is effective and can further improve the performance.
+
+Denoising step number. Tab. 4 shows that due to a reasonable start point, DiffusionDrive achieves good planning quality even with only 1 step, and further denoising steps offer quality improvement and inference flexibility for complex environments.
+
+Cascade stages. Tab. 5 ablates the impact of cascade stage number. Increasing the stage number can improve the planning quality but saturate at the 4 stages and cost more parameters and inference time at each step.
+
+Number of sampled noises  $N_{\mathrm{infer}}$ . As stated in Sec. 3.3, DiffusionDrive can generate varied trajectories by simply sampling a variable number of noises from anchored Gaussian distribution. Tab. 6 shows that 10 sampled noises can already achieve a decent planning quality. By sampling more noises, DiffusionDrive can cover potential planning action space and lead to improved planning quality.
+
+# 4.6. Qualitative Comparison
+
+Since the PDMS planning metric calculates based on the top-1 scoring trajectory and our proposed  $\mathcal{D}$  score evaluates mode diversity, these metrics alone cannot fully capture the
+
+quality of diverse trajectories. To further validate the quality of multi-mode trajectories, we visualize the planning results of Transfuser,  $\mathrm{Transfuser}_{\mathrm{DP}}$  and DiffusionDrive on challenging scenarios of NAVSIM navtest split in Fig. 2. The results indicate that the multi-mode trajectories generated by DiffusionDrive are not only diverse but also of high quality. In Fig. 2a, the top-1 scoring trajectory generated by DiffusionDrive closely resembles the ground-truth trajectory, while the highlighted top-10 scoring trajectory surprisingly tries to perform high-quality lane changing. In Fig. 2b, the highlighted top-10 scoring trajectory also performs a lane change, and a neighboring low-scoring trajectory further interacts with surrounding agents to effectively avoid collisions.
+
+# 4.7. Quantitative Comparison on nuScenes dataset
+
+The nuScenes dataset is previously popular benchmark for end-to-end planning. Since the major scenarios of nuScenes are simple and trivial situations, we only perform comparison in Tab. 7. We implement DiffusionDrive on top of SparseDrive [39] following its training and inference recipe using open-loop metrics proposed in ST-P3 [15]. We stack 2 cascade diffusion decoder layers and apply the truncated diffusion policy with 18 clustered anchors.
+
+As shown in Tab. 7, DiffusionDrive reduces the average L2 error of SparseDrive by  $0.04\mathrm{m}$ , achieving the lowest L2 error and average collision rate. While DiffusionDrive is also efficient and runs  $1.8\times$  faster than VAD with  $20.8\%$  lower L2 error and  $63.6\%$  lower collision rate.
+
+# 5. Conclusion
+
+In this work, we propose a novel generative driving decision-making model, DiffusionDrive, for end-to-end autonomous driving by incorporating the proposed truncated diffusion policy and efficient cascade diffusion decoder. DiffusionDrive can denoise a variable number of samples from an anchored Gaussian distribution to generate diverse planning trajectories at real-time speeds. Comprehensive experiments and qualitative comparisons validate the superiority of DiffusionDrive in planning quality, running efficiency, and mode diversity.
+
+# Acknowledgement
+
+This work was partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 62276108. We would like to acknowledge Tianheng Cheng for helpful feedback on the draft.
+
+# References
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+        "type": "text",
+        "text": "DiffusionSfM: Predicting Structure and Motion via Ray Origin and Endpoint Diffusion",
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+        "text": "Qitao Zhao, Amy Lin, Jeff Tan, Jason Y. Zhang, Deva Ramanan, Shubham Tulsiani Carnegie Mellon University",
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+        "type": "text",
+        "text": "Project page: qitaozhao.github.io/DiffusionSfM",
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+        "image_caption": [
+            "Figure 1. DiffusionSfM. Top: Given a set of multi-view images (left), DiffusionSfM represents scene geometry and cameras (right) as pixel-wise ray origins and endpoints in a global frame. It learns a denoising diffusion model to infer these elements directly from multiview inputs. Unlike traditional Structure-from-Motion (SfM) pipelines, which separate pairwise reasoning and global optimization into two stages, our approach unifies both into a single end-to-end multi-view reasoning framework. Bottom: Example results of inferred scene geometry and cameras for two distinct settings: a real-world outdoor scene (left) and a synthetic indoor scene (right)."
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+        "text": "Abstract",
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+        "type": "text",
+        "text": "Current Structure-from-Motion (SfM) methods typically follow a two-stage pipeline, combining learned or geometric pairwise reasoning with a subsequent global optimization step. In contrast, we propose a data-driven multi-view reasoning approach that directly infers 3D scene geometry and camera poses from multi-view images. Our framework, DiffusionSfM, parameterizes scene geometry and cameras as pixel-wise ray origins and endpoints in a global frame and employs a transformer-based denoising diffusion model to predict them from multi-view inputs. To address practical challenges in training diffusion models with missing data and unbounded scene coordinates, we introduce specialized mechanisms that ensure robust learning. We empirically validate DiffusionSfM on both synthetic and real datasets, demonstrating that it outperforms classical and learning-based approaches while naturally modeling uncertainty.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The task of recovering structure (geometry) and motion (cameras) from multi-view images has long been a focus of the computer vision community, with typical pipelines [25] performing pairwise correspondence estimation followed by global optimization. While classical methods relied on hand-designed features, matching, and optimization, there has been a recent shift towards incorporating learning-based alternatives [5, 6, 14, 23]. More recently, the widely influential DUSt3R [36] advocates for predicting pairwise 3D pointmaps (instead of only correspondences), demonstrating that this can yield accurate dense geometry and cameras. In order to reconstruct more than two views, DUSt3R (and its variants [10]) still require a global optimization reminiscent of classic bundle adjustment. While these methods, both classical and learning-based, have led to impressive improvements in SfM, the overall approach is largely unchanged – learned or geometric pairwise reasoning followed by global optimization. In this work, we",
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+    {
+        "type": "header",
+        "text": "CVF",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            236,
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+    },
+    {
+        "type": "page_number",
+        "text": "6317",
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+    {
+        "type": "text",
+        "text": "seek to develop an alternative approach that directly predicts both structure and motion, unifying pairwise reasoning and global optimization into a single multi-view framework.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We are of course not the first to attempt to find unified alternatives to the two-stage SfM pipeline. In the sparse-view setting where conventional correspondence-based methods struggle, several works employ multi-view architectures to jointly reason across input images. SparsePose [26], RelPose++ [12], and PoseDiffusion [34] all leverage multiview transformers to estimate camera pose for input images, albeit using differing mechanisms such as regression, energy-based modeling, and denoising diffusion. More recently, RayDiffusion [41] argues for a local raymap parameterization of cameras instead of a global extrinsic matrix and shows that existing patch-based transformers can be easily adapted for this task, yielding significantly more accurate pose predictions. Importantly, such methods predict only camera motion and fail to predict scene structure.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this work, we present DiffusionSfM, an end-to-end multi-view model that directly infers dense 3D geometry and cameras from multiple input images. Instead of inferring (depth-agnostic) rays per image patch (as in RayDiffusion [41]) or 3D points per pixel (as in DUSt3R [36]), DiffusionSfM effectively combines both to predict ray origins and endpoints per pixel, directly reporting both scene geometry (endpoints) and generalized cameras (rays). These can readily be converted back to traditional cameras [41]. Compared to RayDiffusion, our model directly predicts structure as well as motion at a finer scale (pixel-wise v.s. patchwise). Compared to DUSt3R, our model directly predicts motion as well as structure but, even more importantly, does so for  $N$  views, eliminating the need for memory-intensive global alignment. To model uncertainty, we train a denoising diffusion model but find two key challenges that need to be addressed. First, diffusion models require (noisy) ground truth as input for training, but existing real datasets do not have known endpoints for all pixels due to missing depth in multi-view stereo. Second, the 3D coordinates of endpoints can be potentially unbounded, whereas diffusion models require normalized data. We develop mechanisms to overcome these challenges, leveraging additional \"GT mask conditioning\" as input to inform the model of missing input data and parameterizing 3D points in projective space instead of Euclidean space. We find these strategies allow us to learn accurate predictions for structure and motion.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We train and evaluate DiffusionSfM on real-world and synthetic datasets [21, 24, 42] and find that it can infer accurate geometry and cameras for both object-centric and scene-level images (see Fig. 1). In particular, we find that DiffusionSfM yields more accurate camera estimates compared to prior work across these settings while also modeling the underlying uncertainty via the diffusion process. In summary, we show that DiffusionSfM can serve as a unified",
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+    {
+        "type": "text",
+        "text": "multi-view reasoning model for 3D geometry and cameras.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Structure from Motion. Structure-from-Motion (SfM) systems [25] aim to simultaneously recover geometry and cameras given a set of input images. The typical SfM pipeline extracts pixel correspondences from keypoint matching [2, 16], and performs global bundle adjustment (BA) to optimize sparse 3D points and camera parameters by minimizing reprojection errors. Recently, SfM pipelines have been substantially enhanced by replacing classical subcomponents with learning-based methods, such as neural feature descriptors [6, 8], keypoint matching [15, 23, 30], and bundle adjustment [13, 32].",
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+        "text": "More recently, an emerging body of research aims to unify the various SfM subcomponents into an end-to-end neural framework. Notably, ACEZero [3] fits a single neural network to input images and learns pixel-aligned 3D coordinates in a self-supervised manner, while FlowMap [27] predicts per-frame cameras and depth maps using off-the-shelf optical flow as supervision. Though ACEZero and FlowMap are promising attempts to revolutionize SfM pipelines, they both register images incrementally and may suffer under large viewpoint changes. DUSt3R [36] directly regresses 3D pointmaps from image pairs and shows strong generalization ability [11, 21]. Building on DUSt3R, MASt3R [10] introduces a feature head, offering pixel-matching capabilities. MASt3R-SfM [7] is a more scalable SfM pipeline based on MASt3R. While these approaches [7, 10, 36] show impressive performance and robustness under sparse views, they are essentially pair-based, requiring sophisticated global alignment procedures to form a consistent estimate for more than two views.",
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+        "type": "text",
+        "text": "Pose Estimation with Global Reasoning. For the task of sparse-view pose estimation, learning-based methods equipped with global reasoning show favorable robustness where traditional SfM methods [25, 28] fail. This line of research includes energy-based [12, 40], regression-based [26], and diffusion-based pose estimators [34, 41]. Among them, diffusion-based methods show a better ability to handle uncertainty [41]. Closest to our work, RayDiffusion [41] leverages a denoising diffusion model [9, 19] with a patch-aligned (depth-unaware) ray representation to predict generic cameras. Our method goes further and pursues a generic representation for both geometry and cameras in the form of ray origins and endpoints for each pixel. In addition to resulting in a richer output, this joint geometry and pose prediction also yields improvements for pose estimation.",
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+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Given a set of sparse (i.e., 2-8) input images, DiffusionSfM predicts the geometry and cameras of a 3D scene in a global",
+        "bbox": [
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+        "text": "6318",
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+    {
+        "type": "image",
+        "img_path": "images/e313265c3ef039eaa8c98aab188fac7c1ec90a35c2ae39191b416a12c793c328.jpg",
+        "image_caption": [
+            "Figure 2. Method. Given sparse multi-view images as input, DiffusionSfM predicts pixel-wise ray origins and endpoints in a global frame (Sec. 3.1) using a denoising diffusion process (Sec. 3.2). For each image, we compute patch-wise embeddings with DINOv2 [18] and embed noisy ray origins and endpoints into latents using a single downsampling convolutional layer, ensuring alignment with the spatial footprint of the image embeddings. We implement a Diffusion Transformer architecture that predicts clean ray origins and endpoints from noisy samples. A convolutional DPT [20] head outputs full-resolution denoised ray origins and endpoints. To handle incomplete ground truth (GT) during training, we condition the model on a GT mask (Sec. 3.3). At inference, the GT mask is set to all ones, enabling the model to predict origins and endpoints for all pixels. The predicted ray origins and endpoints can be directly visualized in 3D or postprocessed to recover camera extrinsics, intrinsics, and multi-view consistent depth maps."
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "coordinate frame. In Sec. 3.1, we propose to represent 3D scenes as dense pixel-aligned ray origins and endpoints. To predict such scene representations from sparse input images while modeling uncertainty, Sec. 3.2 proposes a denoising diffusion architecture. We then discuss some key practical challenges in training such a model in Sec. 3.3.",
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+    {
+        "type": "text",
+        "text": "3.1. 3D Scenes as Ray Origins and Endpoints",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Given an input image  $\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}$  with a depth map  $\\mathbf{D} \\in \\mathbb{R}^{H \\times W}$ , camera intrinsics  $\\mathbf{K} \\in \\mathbb{R}^{3 \\times 3}$ , and world-to-camera extrinsics  $\\mathbf{T} \\in \\mathbb{R}^{4 \\times 4}$  (equivalently, rotation  $\\mathbf{R} \\in SO(3)$  and translation  $\\mathbf{t} \\in \\mathbb{R}^3$ ), each 2D image pixel  $\\mathbf{P}_{ij} = [u, v]$  corresponds to a ray that travels from the camera center  $\\mathbf{c}$  through the pixel's projected position on the image plane, terminating at the object's surface as specified by the depth map  $\\mathbf{D}$ . The endpoint of the ray associated with image pixel  $\\mathbf{P}_{ij}$  is given by:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {E} _ {i j} = \\mathbf {T} ^ {- 1} h (\\mathbf {D} _ {i j} \\cdot \\mathbf {K} ^ {- 1} [ u, v, 1 ] ^ {T}) \\tag {1}\n$$\n",
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+        "type": "text",
+        "text": "where  $h$  maps the 3D point into homogeneous coordinates. The shared ray origin  $\\mathbf{O}_{ij}$  for all pixels is equivalent to the camera center  $\\mathbf{c}$ , and can be computed as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {O} _ {i j} = \\mathbf {c} = h (- \\mathbf {R} ^ {- 1} \\mathbf {t}) \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "In summary, we associate each image pixel with a ray origin and endpoint  $\\mathbf{S}_{ij} = \\langle \\mathbf{O}_{ij},\\mathbf{E}_{ij}\\rangle$  in world coordinates, describing the location of the observing camera and the observed 3D point on the object surface. Given a bundle of ray origins and endpoints, we can easily extract the corresponding camera pose [41].",
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+        "type": "text",
+        "text": "Learning Over-Parameterized Representations. We represent 3D scenes and cameras using distributed ray origins  $\\mathbf{O}$  and endpoints  $\\mathbf{E}$  rather than global alternatives such as quaternions and translation vectors. This design is inspired by RayDiffusion [41], and it facilitates the use of the",
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+    {
+        "type": "text",
+        "text": "distributed deep features learned by state-of-the-art vision backbones, such as DINOv2 [18], which encode image information in a patch-wise manner. Notably, while ray origins  $\\mathbf{O}$  should ideally be identical across all pixels, we predict them densely alongside ray endpoints  $\\mathbf{E}$ . This encourages ray origins to remain close within the same image, providing implicit regularization during training. Practically, predicting both ray origins and endpoints simultaneously is easy to implement using a single projection head.",
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+    {
+        "type": "text",
+        "text": "3.2. DiffusionSfM",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We propose a denoising Diffusion Transformer (DiT) architecture [19] that predicts ray origins and endpoints (Sec. 3.1) via a denoising diffusion process. An overview of DiffusionSfM is given in Fig. 2.",
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+        "type": "text",
+        "text": "Diffusion Framework. Given pixel-aligned ray origins and endpoints  $S = \\text{stack}(\\{\\mathbf{S}^{(n)}\\}_{n=1}^{N})$  associated with a set of  $N$  input images, we apply a forward diffusion process [9, 29] that adds time-dependent Gaussian noise to them. Let  $S_{t}$  denote the noisy ray origins and endpoints at timestep  $t$ , where  $S_{0}$  is the clean sample and  $S_{T}$  (at the final diffusion step  $T$ ) approximates pure Gaussian noise. The forward diffusion process is defined as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathcal {S} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $t \\sim \\mathrm{Uniform}(0, T]$ ,  $\\epsilon \\sim \\mathcal{N}(0, I)$ , and  $\\bar{\\alpha}_t$  follows a pre-defined noise schedule that controls the strength of added noise at each timestep. To perform the reverse diffusion process, which progressively reconstructs the clean sample given noisy observations, we train a diffusion model  $f_\\theta$  that takes  $\\mathcal{S}_t$  as input and optionally incorporates additional conditioning information  $\\mathcal{C}$ . The model is trained using the following loss function (with the \"  $x_0$ \" objective):",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {D i f f u s i o n}} = \\mathbb {E} _ {t, S _ {0}, \\epsilon} \\| S _ {0} - f _ {\\theta} (S _ {t}, t, \\mathcal {C}) \\| ^ {2} \\tag {4}\n$$\n",
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+    {
+        "type": "page_number",
+        "text": "6319",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Architecture. We implement  $f_{\\theta}$  using a DiT [19] architecture conditioned on deep image features  $\\mathcal{C} \\in \\mathbb{R}^{N \\times h \\times w \\times c_1}$  from DINOv2 [18], where  $h$  and  $w$  are the patch resolution and  $c_1$  is the embedding dimension. To align pixels to the spatial information learned by DINOv2, we apply a convolutional layer with kernel size and stride equal to ViT patch size: this spatially downsamples the noisy ray origins and endpoints  $S_t$  to match the DINOv2 features while increasing their feature dimension:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} = \\operatorname {C o n v} \\left(\\mathcal {S} _ {t}\\right) \\in \\mathbb {R} ^ {N \\times h \\times w \\times c _ {2}} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The combined DiT input is constructed by concatenating these two feature sets along the channel dimension:  $\\mathcal{F} \\oplus \\mathcal{C}$ . Within DiT, patch-wise features attend to others through self-attention [33]. To distinguish between different images and their respective patches, we apply sinusoidal positional encoding [33] based on image and patch indices.",
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+        "type": "text",
+        "text": "While the DiT operates on low-resolution features, our objective is to produce pixel-aligned dense ray origins and endpoints. To achieve this, we employ a DPT (Dense Prediction Transformer) [20] decoder, which takes intermediate feature maps from both DINoV2 and DiT as inputs. The DPT decoder progressively increases the feature resolution through several convolutional layers. The final ray origins and endpoints are decoded from the DPT output using a single linear layer. During inference, we apply the trained model in the reverse diffusion process to iteratively denoise a randomly initialized Gaussian sample.",
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+    {
+        "type": "text",
+        "text": "3.3. Practical Training Considerations",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Homogeneous Coordinates for Unbounded Geometry. Real-world scenes often exhibit significant variations in scale, both across different scenes and within a single scene. While normalizing by the average distance of 3D points [36] helps address cross-scene variation, within-scene variations remain. For instance, a background building may be much farther away than foreground elements, potentially resulting in extremely large coordinate values when generating ground-truth ray origins and endpoints. However, neural networks (especially diffusion models) tend to train most effectively when working with bounded inputs and outputs (e.g., between -1 and 1). To stabilize training across the large scale variations present in 3D scene datasets, we propose to represent ray origins and endpoints in homogeneous coordinates. Specifically, given any 3D point, we apply a homogeneous transform from  $\\mathbb{R}^3\\to \\mathbb{P}^3$ :",
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+    {
+        "type": "equation",
+        "text": "\n$$\n(x, y, z) \\rightarrow \\frac {1}{w} (x, y, z, 1) \\tag {6}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $w$  is an arbitrary scale factor. To encourage bounded coordinates in practice, we choose  $w$  such that the homogeneous coordinate is unit-norm:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw := \\sqrt {x ^ {2} + y ^ {2} + z ^ {2} + 1} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unit normalization allows homogeneous coordinates to serve as a bounded representation for unbounded scene geometry. For example,  $(x,y,z,0)$  is a point at infinity in the direction of  $(x,y,z)$ . We find that this representation makes large coordinate values more tractable during training.",
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+    {
+        "type": "text",
+        "text": "Training with Incomplete Ground Truth. Many real-world datasets (e.g., CO3D [21] and MegaDepth [11]), provide only sparse point clouds, leading to incomplete depth information. This presents a significant challenge in diffusion training, as ground-truth (GT) depth values that are used to create clean ray endpoints often contain invalid or missing data. It is highly undesirable for these missing ray endpoints to be interpreted as part of the target distribution. Unlike regression models (e.g., DUSt3R [36]), which do not require (noisy) GT data as input and can simply apply a mask on the loss for supervision, diffusion models must handle incomplete inputs during training.",
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+    },
+    {
+        "type": "text",
+        "text": "To mitigate this issue, we further apply GT masks  $\\mathcal{M} \\in \\mathbb{R}^{N \\times H \\times W}$  to the DiT inputs, where zero values indicate pixels with invalid depth. During training, we multiply DiT inputs with GT masks element-wise, then concatenate along the channel dimension:  $S_{t}' = (\\mathcal{M} \\cdot S_{t}) \\oplus \\mathcal{M}$ . Then, we only compute the diffusion loss in Eq. 4 over unmasked pixels. By implementing these strategies, we encourage the model to focus on regions with valid GT values during training. During inference, however, we would like the diffusion process to estimate ray endpoints at all pixels, so we always use GT masks with values set to one.",
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+    {
+        "type": "text",
+        "text": "Sparse-to-Dense Training. In practice, we find that training the entire model from scratch leads to slow convergence and suboptimal performance. To address this, we propose a sparse-to-dense training approach. First, we train a sparse version of the model, where the DPT decoder is removed, and the output ray origins and endpoints have the same spatial resolution as the DINOv2 features. Unlike Eq. 5, no spatial downsampling is required, so this sparse model uses a single linear layer to embed the noisy ray origins and endpoints. Once the sparse model is trained, we initialize the dense model DiT with the learned weights from the sparse model. This two-stage approach significantly improves performance; see the supplementary material for comparisons.",
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+        "type": "text",
+        "text": "4. Experiments",
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+        "text": "4.1. Experimental Setup",
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+        "type": "text",
+        "text": "Datasets. We introduce two model variants, each trained on different datasets. (1) DiffusionSfM-CO3D: Following prior work [12, 41], we train and evaluate our model on the CO3D dataset [21], which consists of turntable video sequences of various object categories. Specifically, we train on 41 object categories and evaluate on both these seen categories and an additional 10 unseen categories to assess generalization. (2) DiffusionSfM: This variant is trained on the",
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+            "Figure 3. Qualitative Comparison on Camera Pose Accuracy and Predicted Geometry. For each method, we plot the ground-truth cameras in black and the predicted cameras in other colors. DiffusionSfM demonstrates robust performance even with challenging inputs. Compared to DUSt3R, which sometimes fails to register images in a consistent manner, DiffusionSfM consistently yields a coherent global prediction. Additionally, while we observe that DUSt3R can predict highly precise camera rotations, it often struggles with camera centers (see the backpack example). Input images depicting scenes are out-of-distribution for RayDiffusion, as it is trained on CO3D only."
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+        "type": "text",
+        "text": "datasets used for DUSt3R [36], excluding Waymo [31] due to its excessively sparse depth maps. The included datasets are Habitat [24], CO3D [21], ScanNet++ [39], ArkitScenes [1], Static Scenes 3D [17], MegaDepth [11], and BlendedMVS [38]. We follow the DUSt3R official repository [37]",
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+    {
+        "type": "text",
+        "text": "guidelines to extract image pairs, ensuring reasonable overlap between paired images. To construct multi-view data given these pre-computed pairs, we iteratively sample images using an adjacency matrix, maintaining sufficient overlap with the selected set. Beyond CO3D, this model variant",
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+        "image_caption": [
+            "Figure 4. Additional Qualitative Results on Predicted Camera Poses. DiffusionSfM shows robustness to ambiguous patterns in inputs."
+        ],
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+    {
+        "type": "text",
+        "text": "is also evaluated on Habitat and RealEstate10k [42].",
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+    {
+        "type": "text",
+        "text": "Baselines and Metrics. To evaluate camera pose accuracy in the sparse-view setup, we compare with RayDiffusion [41] and DUSt3R [36], along with previous methods [12, 22, 34]. DUSt3R is trained initially on a mixture of eight datasets, while most other baselines are trained only on CO3D. For a fair and comprehensive comparison, we re-train DUSt3R on the 41-10 split of CO3D, using the authors' official implementation [37] and hyperparameters (referred to as DUSt3R-CO3D). To evaluate camera predictions, we follow prior work [41] and convert predicted rays back to traditional extrinsic matrices and report two pose accuracy metrics: (1) Camera Rotation Accuracy which compares the predicted relative camera rotation between images against ground truth and (2) Camera Center Accuracy which compares predicted camera centers to the ground truth after a similarity alignment. To evaluate the estimated geometry (i.e., ray endpoints), we report Chamfer Distance (CD). Additionally, to explore whether combining an off-the-shelf sparse-view pose estimation method (RayDiffusion) with a monocular depth estimation model (MoGe [35]) is sufficient to infer 3D scene geometry from",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "multiple images, we introduce a new baseline,  $\\mathsf{RD} + \\mathsf{MoGe}$ . We include more details in the supplementary. Unless otherwise specified, all evaluations use 2-8 input images.",
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+    {
+        "type": "text",
+        "text": "4.2. Evaluation on CO3D",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Camera Pose Accuracy. We present the quantitative results in Tab. 1. For camera rotation accuracy, both versions of DiffusionSfM outperform all baselines, except that DUSt3R achieves slightly higher overall accuracy than DiffusionSfM-CO3D on unseen categories – likely due to its training on more data. For camera center accuracy, our approach consistently outperforms all other methods. We hypothesize that these gains stem from our explicit modeling of camera centers through ray origin prediction. The qualitative results in Fig. 3 illustrate that DiffusionSfM produces robust predictions given challenging inputs, whereas DUSt3R produces inaccurate results. We attribute this improvement to our model's probabilistic modeling capability derived from diffusion, as well as its multi-view reasoning abilities, which together effectively handle these challenging scenarios. While we observe that DUSt3R can predict highly precise camera rotations, it often struggles with cam-",
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+    {
+        "type": "page_number",
+        "text": "6322",
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+    {
+        "type": "table",
+        "img_path": "images/a33cb5d7197aa3e345a5d224916c27764df2b9ba8ce3e1bee23582ecf8870ce7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\"># of Images</td><td colspan=\"6\">Rotation Accuracy (↑, @ 15°)</td><td colspan=\"7\">Center Accuracy (↑, @ 0.1)</td></tr><tr><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td></tr><tr><td rowspan=\"8\">Seen Categories</td><td>COLMAP [22]</td><td>30.7</td><td>28.4</td><td>26.5</td><td>26.8</td><td>27.0</td><td>28.1</td><td>30.6</td><td>100</td><td>34.5</td><td>23.8</td><td>18.9</td><td>15.6</td><td>14.5</td></tr><tr><td>PoseDiffusion [34]</td><td>75.7</td><td>76.4</td><td>76.8</td><td>77.4</td><td>78.0</td><td>78.7</td><td>78.8</td><td>100</td><td>77.5</td><td>69.7</td><td>65.9</td><td>63.7</td><td>62.8</td></tr><tr><td>RelPose++ [12]</td><td>81.8</td><td>82.8</td><td>84.1</td><td>84.7</td><td>84.9</td><td>85.3</td><td>85.5</td><td>100</td><td>85.0</td><td>78.0</td><td>74.2</td><td>71.9</td><td>70.3</td></tr><tr><td>RayDiffusion [41]</td><td>91.8</td><td>92.4</td><td>92.6</td><td>92.9</td><td>93.1</td><td>93.3</td><td>93.3</td><td>100</td><td>94.2</td><td>90.5</td><td>87.8</td><td>86.2</td><td>85.0</td></tr><tr><td>DUSt3R-CO3D [36]</td><td>86.7</td><td>87.9</td><td>88.0</td><td>88.2</td><td>88.6</td><td>88.8</td><td>88.9</td><td>100</td><td>92.0</td><td>86.8</td><td>83.8</td><td>82.0</td><td>81.1</td></tr><tr><td>DUSt3R [36]</td><td>91.7</td><td>92.7</td><td>93.3</td><td>93.6</td><td>93.8</td><td>94.0</td><td>94.3</td><td>100</td><td>93.0</td><td>85.7</td><td>81.9</td><td>79.6</td><td>77.8</td></tr><tr><td>DiffusionSfM-CO3D</td><td>93.4</td><td>94.0</td><td>94.5</td><td>94.8</td><td>95.0</td><td>95.2</td><td>95.1</td><td>100</td><td>95.9</td><td>93.6</td><td>92.2</td><td>91.2</td><td>90.7</td></tr><tr><td>DiffusionSfM</td><td>92.4</td><td>93.5</td><td>94.0</td><td>94.5</td><td>94.7</td><td>95.1</td><td>95.2</td><td>100</td><td>95.3</td><td>92.9</td><td>91.9</td><td>91.2</td><td>90.8</td></tr><tr><td rowspan=\"8\">Unseen Categories</td><td>COLMAP [22]</td><td>34.5</td><td>31.8</td><td>31.0</td><td>31.7</td><td>32.7</td><td>35.0</td><td>38.5</td><td>100</td><td>36.0</td><td>25.5</td><td>20.0</td><td>17.9</td><td>17.6</td></tr><tr><td>PoseDiffusion [34]</td><td>63.2</td><td>64.2</td><td>64.2</td><td>65.7</td><td>66.2</td><td>67.0</td><td>67.7</td><td>100</td><td>63.6</td><td>50.5</td><td>45.7</td><td>43.0</td><td>41.2</td></tr><tr><td>RelPose++ [12]</td><td>69.8</td><td>71.1</td><td>71.9</td><td>72.8</td><td>73.8</td><td>74.4</td><td>74.9</td><td>100</td><td>70.6</td><td>58.8</td><td>53.4</td><td>50.4</td><td>47.8</td></tr><tr><td>RayDiffusion [41]</td><td>83.5</td><td>85.6</td><td>86.3</td><td>86.9</td><td>87.2</td><td>87.5</td><td>88.1</td><td>100</td><td>87.7</td><td>81.1</td><td>77.0</td><td>74.1</td><td>72.4</td></tr><tr><td>DUSt3R-CO3D [36]</td><td>79.8</td><td>81.5</td><td>82.6</td><td>82.7</td><td>83.0</td><td>83.3</td><td>83.7</td><td>100</td><td>83.6</td><td>77.2</td><td>71.8</td><td>70.0</td><td>68.1</td></tr><tr><td>DUSt3R [36]</td><td>90.8</td><td>92.6</td><td>93.6</td><td>93.6</td><td>93.8</td><td>93.6</td><td>93.4</td><td>100</td><td>87.9</td><td>79.8</td><td>74.3</td><td>71.7</td><td>69.4</td></tr><tr><td>DiffusionSfM-CO3D</td><td>90.4</td><td>91.2</td><td>92.7</td><td>93.0</td><td>93.1</td><td>93.3</td><td>93.5</td><td>100</td><td>91.1</td><td>87.7</td><td>85.3</td><td>83.7</td><td>82.7</td></tr><tr><td>DiffusionSfM</td><td>91.5</td><td>92.8</td><td>93.6</td><td>93.9</td><td>94.1</td><td>94.2</td><td>94.4</td><td>100</td><td>92.4</td><td>87.9</td><td>86.2</td><td>85.3</td><td>84.1</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "era centers (see the backpack example). Additional qualitative results on camera accuracy are provided in Fig.4.",
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+    {
+        "type": "text",
+        "text": "Predicted Geometry. To evaluate predicted geometry, we compute Chamfer Distance (CD) and show comparisons against baselines in Tab. 2. We compute CD in two setups (with and without foreground object mask), and find that DiffusionSfM-CO3D performs best without foreground masking. In this setup, the predicted ray endpoints corresponding to the background image pixels tend to have larger coordinate values than foreground ones, and therefore dominate CD. This result indicates that our model provides more accurate predictions for complex image backgrounds. In terms of CD with masking, DUSt3R achieves the best result, while our two model variants outperform DUSt3R-CO3D. See Fig. 3 for visualization. We also notice that naively combining RayDiffusion poses with estimated depths from MoGe does not work well, as the inferred depths are potentially inconsistent across different views, thus resulting in degraded performance.",
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+    {
+        "type": "text",
+        "text": "4.3. Evaluation on Scene-Level Datasets",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Beyond the object-centric CO3D dataset [21], we compare DiffusionSfM against DUSt3R on two scene-level datasets: Habitat (in-distribution) [24] and RealEstate10k (out-of-distribution) [42]. The results are presented in Tab. 3. While DiffusionSfM achieves comparable camera rotation accuracy to DUSt3R, it consistently predicts more accurate camera centers, aligning with our findings on CO3D.",
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+    {
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+        "table_caption": [
+            "Table 1. Camera Rotation and Center Accuracy on CO3D. On the left, we report the proportion of relative camera rotations within  $15^{\\circ}$  of the ground truth. On the right, we report the proportion of camera centers within  $10\\%$  of the scene scale, relative to the ground truth. To align the predicted camera centers to ground truth, we apply an optimal similarity transform  $(s, \\mathbf{R}, \\mathbf{t})$ , hence the alignment is perfect at  $N = 2$  but worsens with more images. DiffusionSfM outperforms all other methods for camera center accuracy, and outperforms all methods trained on equivalent data for rotation accuracy."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td># of Images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>RD*+MoGe [41]</td><td>0.059</td><td>0.064</td><td>0.071</td><td>0.062</td><td>0.063</td><td>0.061</td><td>0.061</td></tr><tr><td>DUSt3R* [36]</td><td>0.036</td><td>0.037</td><td>0.040</td><td>0.040</td><td>0.037</td><td>0.036</td><td>0.039</td></tr><tr><td>DUSt3R [36]</td><td>0.021</td><td>0.023</td><td>0.024</td><td>0.024</td><td>0.025</td><td>0.025</td><td>0.023</td></tr><tr><td>DiffusionSfM*</td><td>0.019</td><td>0.021</td><td>0.022</td><td>0.022</td><td>0.021</td><td>0.021</td><td>0.021</td></tr><tr><td>DiffusionSfM</td><td>0.025</td><td>0.025</td><td>0.025</td><td>0.025</td><td>0.026</td><td>0.025</td><td>0.028</td></tr><tr><td>RD*+MoGe [41]</td><td>0.071</td><td>0.075</td><td>0.068</td><td>0.067</td><td>0.066</td><td>0.064</td><td>0.064</td></tr><tr><td>DUSt3R* [36]</td><td>0.038</td><td>0.036</td><td>0.036</td><td>0.036</td><td>0.034</td><td>0.033</td><td>0.034</td></tr><tr><td>DUSt3R [36]</td><td>0.023</td><td>0.022</td><td>0.019</td><td>0.020</td><td>0.019</td><td>0.020</td><td>0.020</td></tr><tr><td>DiffusionSfM*</td><td>0.028</td><td>0.025</td><td>0.024</td><td>0.024</td><td>0.024</td><td>0.023</td><td>0.022</td></tr><tr><td>DiffusionSfM</td><td>0.027</td><td>0.024</td><td>0.023</td><td>0.022</td><td>0.022</td><td>0.022</td><td>0.021</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2. Chamfer Distance  $(\\downarrow)$  on CO3D Unseen Categories. Top: CD computed on all scene points. Bottom: CD computed on foreground points only. Models marked with “*” are trained on CO3D only, while those without are trained on multiple datasets. Note that top and bottom values are not directly comparable, as each ground-truth point cloud is individually normalized.",
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+    {
+        "type": "text",
+        "text": "4.4. Inference Speed",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Though our method requires iterative diffusion denoising at inference, we can speed this up by performing early stopping. Specifically, we can treat the  $x_0$ -prediction from early timesteps as our output instead of iterating over all denoising timesteps. Consistent with observations by Zhang et al. [41], this in fact yields more accurate predictions than the final-step diffusion outputs. As a result we only require 10 denoising diffusion timesteps for inference, taking 1.91",
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+        "img_path": "images/a5b3d4e308ef80db7d45571ba6f502b036de286a0336817e442fa29c3ab997cf.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Hab.</td><td>DUSt3R</td><td>97.0/100</td><td>95.0/97.6</td><td>94.3/95.0</td><td>94.2/93.1</td></tr><tr><td>DiffusionSfM</td><td>92.6/100</td><td>93.7/99.1</td><td>94.2/98.8</td><td>94.9/98.6</td></tr><tr><td rowspan=\"2\">RE10</td><td>DUSt3R</td><td>98.1/100</td><td>97.7/68.7</td><td>97.6/57.9</td><td>97.7/53.3</td></tr><tr><td>DiffusionSfM</td><td>97.8/100</td><td>97.5/75.6</td><td>97.7/66.2</td><td>97.9/61.9</td></tr></table>",
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+        "img_path": "images/218890669fb73a4f9cd99bd9c950b2301f5873ae02015299bbe805c9375c2644.jpg",
+        "table_caption": [
+            "Table 3. Camera Rotation and Center Accuracy on Two Scene-Level Datasets. Top: Habitat (2-5 views). Bottom: RealEstate10k (2, 4, 6, 8 views). Each grid reports camera rotation accuracy (left,  $\\uparrow$ ) and center accuracy (right,  $\\uparrow$ ). While DiffusionSfM performs on par with DUSt3R in rotation accuracy, it consistently surpasses DUSt3R in center accuracy."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td># of Images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>DiffusionSfM*</td><td>0.019</td><td>0.021</td><td>0.022</td><td>0.022</td><td>0.021</td><td>0.021</td><td>0.021</td></tr><tr><td>w/o Mask</td><td>0.020</td><td>0.022</td><td>0.023</td><td>0.023</td><td>0.022</td><td>0.022</td><td>0.024</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 4. Ablation Study on GT Mask Conditioning for CO3D Unseen Categories. We assess the effect of replacing GT mask conditioning with depth interpolation in our CO3D variant (DiffusionSfM*), by reporting the CD for predicted geometry. Incorporating mask conditioning to indicate missing data during training improves geometry quality.",
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+    {
+        "type": "text",
+        "text": "seconds on a single A5000 GPU with 8 input images. In contrast, DUSt3R takes 8.73 seconds to run the complete pairwise inference and global alignment procedure. We provide additional analysis in the supplementary material.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Homogeneous Coordinates. The use of homogeneous coordinates for ray origins and endpoints is crucial for stable model training. To assess its impact, we replace the proposed homogeneous representation with standard 3D coordinates in  $\\mathbb{R}^3$ . Our experiments show that this variant is difficult to train and fails to converge. Further details on this experiment are provided in the supplementary material.",
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+    },
+    {
+        "type": "text",
+        "text": "GT Mask Conditioning. To evaluate the effectiveness of the proposed GT mask conditioning, we train a baseline model without using this strategy. For missing values in the ground-truth depth maps, we use nearest-neighbor interpolation to fill in invalid pixels. This experiment is conducted on the CO3D dataset, with results presented in Tab. 4. The findings show that removing GT mask conditioning consistently degrades predicted geometry across varying numbers of input views, even when the loss is still masked. While interpolation can effectively fill missing depth within object regions, it often introduces substantial noise in the background (e.g., the sky). This noise negatively impacts diffusion model training, as the entire ray origin and endpoint maps are used as input. We anticipate an even larger performance gap on non-object-centric datasets with more outdoor scenes, such as MegaDepth [11].",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/73e85658c1c87772133020c3736a2822b53d306c91f74b826fc325128df9097e.jpg",
+        "image_caption": [
+            "Figure 5. Multi-modality of DiffusionSfM. We show two distinct samples from DiffusionSfM, starting from the same input images but with different random noise. Sample 1 explains the input images by putting all flowers on the left side, while Sample 2 places one flower on each side (note the difference in the green camera's viewpoint). DiffusionSfM is able to predict multi-modal geometry distributions when the scene layout is ambiguous in the inputs."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.6. Multi-modality from Multiple Sampling",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Diffusion models enable the generation of diverse samples from challenging input images. For instance, in Fig. 5, the vase exhibits symmetric patterns, and we present two distinct predicted endpoints from DiffusionSfM, each offering a different interpretation of the flowers in the image. Compared to regression models such as DUSt3R [8], DiffusionSfM is better suited for handling uncertainty – an inherent aspect of our task – where a sparse set of input images can correspond to multiple plausible 3D scene geometry.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5. Discussion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We present DiffusionSfM and demonstrate that it recovers accurate predictions of both cameras and geometry from multi-view inputs. Although our results are promising, several challenges and open questions remain.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Notably, DiffusionSfM employs a pixel-space diffusion model, in contrast to the latent-space models adopted by state-of-the-art T2I generative systems. Operating in pixel space may require greater model capacity, yet our current model remains relatively small - potentially explaining the noisy patterns observed along object boundaries. Learning an expressive latent space for ray origins and endpoints by training a VAE could be a promising direction for future work. In addition, the compute requirement in multi-view transformers scales quadratically with the number of input images: one would require masked attention to deploy systems like ours for a large set of input images.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Despite these challenges, we believe that our work highlights the potential of a unified approach for multi-view geometry tasks. We envision that our approach can be built upon to train a common system across related geometric tasks, such as SfM (input images with unknown origins and endpoints), registration (some images have known origins and endpoints, whereas others don't), mapping (known rays but unknown endpoints), and view synthesis (unknown pixel values for known rays).",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "6324",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements: We thank the members of the Physical Perception Lab at CMU for their valuable discussions, and extend special thanks to Yanbo Xu for his insights on diffusion models.",
+        "bbox": [
+            89,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work used Bridges-2 [4] at Pittsburgh Supercomputing Center through allocation CIS240166 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296. This work was supported by Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government.",
+        "bbox": [
+            89,
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+        "page_idx": 8
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+            "content": "Project page: qitaozhao.github.io/DiffusionSfM"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.092,
+                0.27,
+                0.907,
+                0.499
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.089,
+                0.508,
+                0.908,
+                0.581
+            ],
+            "angle": 0,
+            "content": "Figure 1. DiffusionSfM. Top: Given a set of multi-view images (left), DiffusionSfM represents scene geometry and cameras (right) as pixel-wise ray origins and endpoints in a global frame. It learns a denoising diffusion model to infer these elements directly from multiview inputs. Unlike traditional Structure-from-Motion (SfM) pipelines, which separate pairwise reasoning and global optimization into two stages, our approach unifies both into a single end-to-end multi-view reasoning framework. Bottom: Example results of inferred scene geometry and cameras for two distinct settings: a real-world outdoor scene (left) and a synthetic indoor scene (right)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.249,
+                0.598,
+                0.327,
+                0.614
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.643,
+                0.486,
+                0.886
+            ],
+            "angle": 0,
+            "content": "Current Structure-from-Motion (SfM) methods typically follow a two-stage pipeline, combining learned or geometric pairwise reasoning with a subsequent global optimization step. In contrast, we propose a data-driven multi-view reasoning approach that directly infers 3D scene geometry and camera poses from multi-view images. Our framework, DiffusionSfM, parameterizes scene geometry and cameras as pixel-wise ray origins and endpoints in a global frame and employs a transformer-based denoising diffusion model to predict them from multi-view inputs. To address practical challenges in training diffusion models with missing data and unbounded scene coordinates, we introduce specialized mechanisms that ensure robust learning. We empirically validate DiffusionSfM on both synthetic and real datasets, demonstrating that it outperforms classical and learning-based approaches while naturally modeling uncertainty."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.515,
+                0.598,
+                0.645,
+                0.614
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.63,
+                0.909,
+                0.904
+            ],
+            "angle": 0,
+            "content": "The task of recovering structure (geometry) and motion (cameras) from multi-view images has long been a focus of the computer vision community, with typical pipelines [25] performing pairwise correspondence estimation followed by global optimization. While classical methods relied on hand-designed features, matching, and optimization, there has been a recent shift towards incorporating learning-based alternatives [5, 6, 14, 23]. More recently, the widely influential DUSt3R [36] advocates for predicting pairwise 3D pointmaps (instead of only correspondences), demonstrating that this can yield accurate dense geometry and cameras. In order to reconstruct more than two views, DUSt3R (and its variants [10]) still require a global optimization reminiscent of classic bundle adjustment. While these methods, both classical and learning-based, have led to impressive improvements in SfM, the overall approach is largely unchanged – learned or geometric pairwise reasoning followed by global optimization. In this work, we"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6317"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.482,
+                0.137
+            ],
+            "angle": 0,
+            "content": "seek to develop an alternative approach that directly predicts both structure and motion, unifying pairwise reasoning and global optimization into a single multi-view framework."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.14,
+                0.483,
+                0.366
+            ],
+            "angle": 0,
+            "content": "We are of course not the first to attempt to find unified alternatives to the two-stage SfM pipeline. In the sparse-view setting where conventional correspondence-based methods struggle, several works employ multi-view architectures to jointly reason across input images. SparsePose [26], RelPose++ [12], and PoseDiffusion [34] all leverage multiview transformers to estimate camera pose for input images, albeit using differing mechanisms such as regression, energy-based modeling, and denoising diffusion. More recently, RayDiffusion [41] argues for a local raymap parameterization of cameras instead of a global extrinsic matrix and shows that existing patch-based transformers can be easily adapted for this task, yielding significantly more accurate pose predictions. Importantly, such methods predict only camera motion and fail to predict scene structure."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.093,
+                0.37,
+                0.483,
+                0.777
+            ],
+            "angle": 0,
+            "content": "In this work, we present DiffusionSfM, an end-to-end multi-view model that directly infers dense 3D geometry and cameras from multiple input images. Instead of inferring (depth-agnostic) rays per image patch (as in RayDiffusion [41]) or 3D points per pixel (as in DUSt3R [36]), DiffusionSfM effectively combines both to predict ray origins and endpoints per pixel, directly reporting both scene geometry (endpoints) and generalized cameras (rays). These can readily be converted back to traditional cameras [41]. Compared to RayDiffusion, our model directly predicts structure as well as motion at a finer scale (pixel-wise v.s. patchwise). Compared to DUSt3R, our model directly predicts motion as well as structure but, even more importantly, does so for \\(N\\) views, eliminating the need for memory-intensive global alignment. To model uncertainty, we train a denoising diffusion model but find two key challenges that need to be addressed. First, diffusion models require (noisy) ground truth as input for training, but existing real datasets do not have known endpoints for all pixels due to missing depth in multi-view stereo. Second, the 3D coordinates of endpoints can be potentially unbounded, whereas diffusion models require normalized data. We develop mechanisms to overcome these challenges, leveraging additional \"GT mask conditioning\" as input to inform the model of missing input data and parameterizing 3D points in projective space instead of Euclidean space. We find these strategies allow us to learn accurate predictions for structure and motion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.78,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We train and evaluate DiffusionSfM on real-world and synthetic datasets [21, 24, 42] and find that it can infer accurate geometry and cameras for both object-centric and scene-level images (see Fig. 1). In particular, we find that DiffusionSfM yields more accurate camera estimates compared to prior work across these settings while also modeling the underlying uncertainty via the diffusion process. In summary, we show that DiffusionSfM can serve as a unified"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.514,
+                0.092,
+                0.902,
+                0.107
+            ],
+            "angle": 0,
+            "content": "multi-view reasoning model for 3D geometry and cameras."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.122,
+                0.655,
+                0.138
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.148,
+                0.905,
+                0.314
+            ],
+            "angle": 0,
+            "content": "Structure from Motion. Structure-from-Motion (SfM) systems [25] aim to simultaneously recover geometry and cameras given a set of input images. The typical SfM pipeline extracts pixel correspondences from keypoint matching [2, 16], and performs global bundle adjustment (BA) to optimize sparse 3D points and camera parameters by minimizing reprojection errors. Recently, SfM pipelines have been substantially enhanced by replacing classical subcomponents with learning-based methods, such as neural feature descriptors [6, 8], keypoint matching [15, 23, 30], and bundle adjustment [13, 32]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.315,
+                0.905,
+                0.6
+            ],
+            "angle": 0,
+            "content": "More recently, an emerging body of research aims to unify the various SfM subcomponents into an end-to-end neural framework. Notably, ACEZero [3] fits a single neural network to input images and learns pixel-aligned 3D coordinates in a self-supervised manner, while FlowMap [27] predicts per-frame cameras and depth maps using off-the-shelf optical flow as supervision. Though ACEZero and FlowMap are promising attempts to revolutionize SfM pipelines, they both register images incrementally and may suffer under large viewpoint changes. DUSt3R [36] directly regresses 3D pointmaps from image pairs and shows strong generalization ability [11, 21]. Building on DUSt3R, MASt3R [10] introduces a feature head, offering pixel-matching capabilities. MASt3R-SfM [7] is a more scalable SfM pipeline based on MASt3R. While these approaches [7, 10, 36] show impressive performance and robustness under sparse views, they are essentially pair-based, requiring sophisticated global alignment procedures to form a consistent estimate for more than two views."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.603,
+                0.905,
+                0.83
+            ],
+            "angle": 0,
+            "content": "Pose Estimation with Global Reasoning. For the task of sparse-view pose estimation, learning-based methods equipped with global reasoning show favorable robustness where traditional SfM methods [25, 28] fail. This line of research includes energy-based [12, 40], regression-based [26], and diffusion-based pose estimators [34, 41]. Among them, diffusion-based methods show a better ability to handle uncertainty [41]. Closest to our work, RayDiffusion [41] leverages a denoising diffusion model [9, 19] with a patch-aligned (depth-unaware) ray representation to predict generic cameras. Our method goes further and pursues a generic representation for both geometry and cameras in the form of ray origins and endpoints for each pixel. In addition to resulting in a richer output, this joint geometry and pose prediction also yields improvements for pose estimation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.845,
+                0.605,
+                0.86
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.871,
+                0.905,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Given a set of sparse (i.e., 2-8) input images, DiffusionSfM predicts the geometry and cameras of a 3D scene in a global"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6318"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.095,
+                0.089,
+                0.91,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.089,
+                0.226,
+                0.907,
+                0.337
+            ],
+            "angle": 0,
+            "content": "Figure 2. Method. Given sparse multi-view images as input, DiffusionSfM predicts pixel-wise ray origins and endpoints in a global frame (Sec. 3.1) using a denoising diffusion process (Sec. 3.2). For each image, we compute patch-wise embeddings with DINOv2 [18] and embed noisy ray origins and endpoints into latents using a single downsampling convolutional layer, ensuring alignment with the spatial footprint of the image embeddings. We implement a Diffusion Transformer architecture that predicts clean ray origins and endpoints from noisy samples. A convolutional DPT [20] head outputs full-resolution denoised ray origins and endpoints. To handle incomplete ground truth (GT) during training, we condition the model on a GT mask (Sec. 3.3). At inference, the GT mask is set to all ones, enabling the model to predict origins and endpoints for all pixels. The predicted ray origins and endpoints can be directly visualized in 3D or postprocessed to recover camera extrinsics, intrinsics, and multi-view consistent depth maps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.364,
+                0.484,
+                0.455
+            ],
+            "angle": 0,
+            "content": "coordinate frame. In Sec. 3.1, we propose to represent 3D scenes as dense pixel-aligned ray origins and endpoints. To predict such scene representations from sparse input images while modeling uncertainty, Sec. 3.2 proposes a denoising diffusion architecture. We then discuss some key practical challenges in training such a model in Sec. 3.3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.463,
+                0.441,
+                0.479
+            ],
+            "angle": 0,
+            "content": "3.1. 3D Scenes as Ray Origins and Endpoints"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.483,
+                0.484,
+                0.621
+            ],
+            "angle": 0,
+            "content": "Given an input image \\(\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}\\) with a depth map \\(\\mathbf{D} \\in \\mathbb{R}^{H \\times W}\\), camera intrinsics \\(\\mathbf{K} \\in \\mathbb{R}^{3 \\times 3}\\), and world-to-camera extrinsics \\(\\mathbf{T} \\in \\mathbb{R}^{4 \\times 4}\\) (equivalently, rotation \\(\\mathbf{R} \\in SO(3)\\) and translation \\(\\mathbf{t} \\in \\mathbb{R}^3\\)), each 2D image pixel \\(\\mathbf{P}_{ij} = [u, v]\\) corresponds to a ray that travels from the camera center \\(\\mathbf{c}\\) through the pixel's projected position on the image plane, terminating at the object's surface as specified by the depth map \\(\\mathbf{D}\\). The endpoint of the ray associated with image pixel \\(\\mathbf{P}_{ij}\\) is given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.167,
+                0.628,
+                0.482,
+                0.647
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {E} _ {i j} = \\mathbf {T} ^ {- 1} h (\\mathbf {D} _ {i j} \\cdot \\mathbf {K} ^ {- 1} [ u, v, 1 ] ^ {T}) \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.655,
+                0.483,
+                0.7
+            ],
+            "angle": 0,
+            "content": "where \\( h \\) maps the 3D point into homogeneous coordinates. The shared ray origin \\( \\mathbf{O}_{ij} \\) for all pixels is equivalent to the camera center \\( \\mathbf{c} \\), and can be computed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.205,
+                0.709,
+                0.482,
+                0.727
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {O} _ {i j} = \\mathbf {c} = h (- \\mathbf {R} ^ {- 1} \\mathbf {t}) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.735,
+                0.483,
+                0.825
+            ],
+            "angle": 0,
+            "content": "In summary, we associate each image pixel with a ray origin and endpoint \\(\\mathbf{S}_{ij} = \\langle \\mathbf{O}_{ij},\\mathbf{E}_{ij}\\rangle\\) in world coordinates, describing the location of the observing camera and the observed 3D point on the object surface. Given a bundle of ray origins and endpoints, we can easily extract the corresponding camera pose [41]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.826,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Learning Over-Parameterized Representations. We represent 3D scenes and cameras using distributed ray origins \\(\\mathbf{O}\\) and endpoints \\(\\mathbf{E}\\) rather than global alternatives such as quaternions and translation vectors. This design is inspired by RayDiffusion [41], and it facilitates the use of the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.364,
+                0.907,
+                0.501
+            ],
+            "angle": 0,
+            "content": "distributed deep features learned by state-of-the-art vision backbones, such as DINOv2 [18], which encode image information in a patch-wise manner. Notably, while ray origins \\(\\mathbf{O}\\) should ideally be identical across all pixels, we predict them densely alongside ray endpoints \\(\\mathbf{E}\\). This encourages ray origins to remain close within the same image, providing implicit regularization during training. Practically, predicting both ray origins and endpoints simultaneously is easy to implement using a single projection head."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.508,
+                0.655,
+                0.523
+            ],
+            "angle": 0,
+            "content": "3.2. DiffusionSfM"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.53,
+                0.906,
+                0.59
+            ],
+            "angle": 0,
+            "content": "We propose a denoising Diffusion Transformer (DiT) architecture [19] that predicts ray origins and endpoints (Sec. 3.1) via a denoising diffusion process. An overview of DiffusionSfM is given in Fig. 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.591,
+                0.907,
+                0.711
+            ],
+            "angle": 0,
+            "content": "Diffusion Framework. Given pixel-aligned ray origins and endpoints \\( S = \\text{stack}(\\{\\mathbf{S}^{(n)}\\}_{n=1}^{N}) \\) associated with a set of \\( N \\) input images, we apply a forward diffusion process [9, 29] that adds time-dependent Gaussian noise to them. Let \\( S_{t} \\) denote the noisy ray origins and endpoints at timestep \\( t \\), where \\( S_{0} \\) is the clean sample and \\( S_{T} \\) (at the final diffusion step \\( T \\)) approximates pure Gaussian noise. The forward diffusion process is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.619,
+                0.722,
+                0.905,
+                0.739
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {S} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathcal {S} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.75,
+                0.907,
+                0.871
+            ],
+            "angle": 0,
+            "content": "where \\(t \\sim \\mathrm{Uniform}(0, T]\\), \\(\\epsilon \\sim \\mathcal{N}(0, I)\\), and \\(\\bar{\\alpha}_t\\) follows a pre-defined noise schedule that controls the strength of added noise at each timestep. To perform the reverse diffusion process, which progressively reconstructs the clean sample given noisy observations, we train a diffusion model \\(f_\\theta\\) that takes \\(\\mathcal{S}_t\\) as input and optionally incorporates additional conditioning information \\(\\mathcal{C}\\). The model is trained using the following loss function (with the \" \\(x_0 \\)\" objective):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.579,
+                0.885,
+                0.905,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {D i f f u s i o n}} = \\mathbb {E} _ {t, S _ {0}, \\epsilon} \\| S _ {0} - f _ {\\theta} (S _ {t}, t, \\mathcal {C}) \\| ^ {2} \\tag {4}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6319"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.482,
+                0.227
+            ],
+            "angle": 0,
+            "content": "Architecture. We implement \\( f_{\\theta} \\) using a DiT [19] architecture conditioned on deep image features \\( \\mathcal{C} \\in \\mathbb{R}^{N \\times h \\times w \\times c_1} \\) from DINOv2 [18], where \\( h \\) and \\( w \\) are the patch resolution and \\( c_1 \\) is the embedding dimension. To align pixels to the spatial information learned by DINOv2, we apply a convolutional layer with kernel size and stride equal to ViT patch size: this spatially downsamples the noisy ray origins and endpoints \\( S_t \\) to match the DINOv2 features while increasing their feature dimension:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.18,
+                0.235,
+                0.483,
+                0.253
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {F} = \\operatorname {C o n v} \\left(\\mathcal {S} _ {t}\\right) \\in \\mathbb {R} ^ {N \\times h \\times w \\times c _ {2}} \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.261,
+                0.483,
+                0.351
+            ],
+            "angle": 0,
+            "content": "The combined DiT input is constructed by concatenating these two feature sets along the channel dimension: \\(\\mathcal{F} \\oplus \\mathcal{C}\\). Within DiT, patch-wise features attend to others through self-attention [33]. To distinguish between different images and their respective patches, we apply sinusoidal positional encoding [33] based on image and patch indices."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.352,
+                0.484,
+                0.518
+            ],
+            "angle": 0,
+            "content": "While the DiT operates on low-resolution features, our objective is to produce pixel-aligned dense ray origins and endpoints. To achieve this, we employ a DPT (Dense Prediction Transformer) [20] decoder, which takes intermediate feature maps from both DINoV2 and DiT as inputs. The DPT decoder progressively increases the feature resolution through several convolutional layers. The final ray origins and endpoints are decoded from the DPT output using a single linear layer. During inference, we apply the trained model in the reverse diffusion process to iteratively denoise a randomly initialized Gaussian sample."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.526,
+                0.388,
+                0.541
+            ],
+            "angle": 0,
+            "content": "3.3. Practical Training Considerations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.548,
+                0.483,
+                0.789
+            ],
+            "angle": 0,
+            "content": "Homogeneous Coordinates for Unbounded Geometry. Real-world scenes often exhibit significant variations in scale, both across different scenes and within a single scene. While normalizing by the average distance of 3D points [36] helps address cross-scene variation, within-scene variations remain. For instance, a background building may be much farther away than foreground elements, potentially resulting in extremely large coordinate values when generating ground-truth ray origins and endpoints. However, neural networks (especially diffusion models) tend to train most effectively when working with bounded inputs and outputs (e.g., between -1 and 1). To stabilize training across the large scale variations present in 3D scene datasets, we propose to represent ray origins and endpoints in homogeneous coordinates. Specifically, given any 3D point, we apply a homogeneous transform from \\(\\mathbb{R}^3\\to \\mathbb{P}^3\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.203,
+                0.797,
+                0.483,
+                0.825
+            ],
+            "angle": 0,
+            "content": "\\[\n(x, y, z) \\rightarrow \\frac {1}{w} (x, y, z, 1) \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.832,
+                0.484,
+                0.876
+            ],
+            "angle": 0,
+            "content": "where \\( w \\) is an arbitrary scale factor. To encourage bounded coordinates in practice, we choose \\( w \\) such that the homogeneous coordinate is unit-norm:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.199,
+                0.884,
+                0.483,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\nw := \\sqrt {x ^ {2} + y ^ {2} + z ^ {2} + 1} \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.092,
+                0.905,
+                0.168
+            ],
+            "angle": 0,
+            "content": "Unit normalization allows homogeneous coordinates to serve as a bounded representation for unbounded scene geometry. For example, \\((x,y,z,0)\\) is a point at infinity in the direction of \\((x,y,z)\\). We find that this representation makes large coordinate values more tractable during training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.168,
+                0.905,
+                0.349
+            ],
+            "angle": 0,
+            "content": "Training with Incomplete Ground Truth. Many real-world datasets (e.g., CO3D [21] and MegaDepth [11]), provide only sparse point clouds, leading to incomplete depth information. This presents a significant challenge in diffusion training, as ground-truth (GT) depth values that are used to create clean ray endpoints often contain invalid or missing data. It is highly undesirable for these missing ray endpoints to be interpreted as part of the target distribution. Unlike regression models (e.g., DUSt3R [36]), which do not require (noisy) GT data as input and can simply apply a mask on the loss for supervision, diffusion models must handle incomplete inputs during training."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "To mitigate this issue, we further apply GT masks \\(\\mathcal{M} \\in \\mathbb{R}^{N \\times H \\times W}\\) to the DiT inputs, where zero values indicate pixels with invalid depth. During training, we multiply DiT inputs with GT masks element-wise, then concatenate along the channel dimension: \\(S_{t}' = (\\mathcal{M} \\cdot S_{t}) \\oplus \\mathcal{M}\\). Then, we only compute the diffusion loss in Eq. 4 over unmasked pixels. By implementing these strategies, we encourage the model to focus on regions with valid GT values during training. During inference, however, we would like the diffusion process to estimate ray endpoints at all pixels, so we always use GT masks with values set to one."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Sparse-to-Dense Training. In practice, we find that training the entire model from scratch leads to slow convergence and suboptimal performance. To address this, we propose a sparse-to-dense training approach. First, we train a sparse version of the model, where the DPT decoder is removed, and the output ray origins and endpoints have the same spatial resolution as the DINOv2 features. Unlike Eq. 5, no spatial downsampling is required, so this sparse model uses a single linear layer to embed the noisy ray origins and endpoints. Once the sparse model is trained, we initialize the dense model DiT with the learned weights from the sparse model. This two-stage approach significantly improves performance; see the supplementary material for comparisons."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4. Experiments"
+        },
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+            "type": "title",
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+            "content": "4.1. Experimental Setup"
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+            "content": "Datasets. We introduce two model variants, each trained on different datasets. (1) DiffusionSfM-CO3D: Following prior work [12, 41], we train and evaluate our model on the CO3D dataset [21], which consists of turntable video sequences of various object categories. Specifically, we train on 41 object categories and evaluate on both these seen categories and an additional 10 unseen categories to assess generalization. (2) DiffusionSfM: This variant is trained on the"
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+        },
+        {
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Figure 3. Qualitative Comparison on Camera Pose Accuracy and Predicted Geometry. For each method, we plot the ground-truth cameras in black and the predicted cameras in other colors. DiffusionSfM demonstrates robust performance even with challenging inputs. Compared to DUSt3R, which sometimes fails to register images in a consistent manner, DiffusionSfM consistently yields a coherent global prediction. Additionally, while we observe that DUSt3R can predict highly precise camera rotations, it often struggles with camera centers (see the backpack example). Input images depicting scenes are out-of-distribution for RayDiffusion, as it is trained on CO3D only."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "datasets used for DUSt3R [36], excluding Waymo [31] due to its excessively sparse depth maps. The included datasets are Habitat [24], CO3D [21], ScanNet++ [39], ArkitScenes [1], Static Scenes 3D [17], MegaDepth [11], and BlendedMVS [38]. We follow the DUSt3R official repository [37]"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "guidelines to extract image pairs, ensuring reasonable overlap between paired images. To construct multi-view data given these pre-computed pairs, we iteratively sample images using an adjacency matrix, maintaining sufficient overlap with the selected set. Beyond CO3D, this model variant"
+        },
+        {
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+            "content": "Input Images"
+        },
+        {
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+        {
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+            "angle": 0,
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+        {
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+            "angle": 0,
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+        {
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+            "angle": 0,
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+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 4. Additional Qualitative Results on Predicted Camera Poses. DiffusionSfM shows robustness to ambiguous patterns in inputs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.556,
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+            "angle": 0,
+            "content": "is also evaluated on Habitat and RealEstate10k [42]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.584,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Baselines and Metrics. To evaluate camera pose accuracy in the sparse-view setup, we compare with RayDiffusion [41] and DUSt3R [36], along with previous methods [12, 22, 34]. DUSt3R is trained initially on a mixture of eight datasets, while most other baselines are trained only on CO3D. For a fair and comprehensive comparison, we re-train DUSt3R on the 41-10 split of CO3D, using the authors' official implementation [37] and hyperparameters (referred to as DUSt3R-CO3D). To evaluate camera predictions, we follow prior work [41] and convert predicted rays back to traditional extrinsic matrices and report two pose accuracy metrics: (1) Camera Rotation Accuracy which compares the predicted relative camera rotation between images against ground truth and (2) Camera Center Accuracy which compares predicted camera centers to the ground truth after a similarity alignment. To evaluate the estimated geometry (i.e., ray endpoints), we report Chamfer Distance (CD). Additionally, to explore whether combining an off-the-shelf sparse-view pose estimation method (RayDiffusion) with a monocular depth estimation model (MoGe [35]) is sufficient to infer 3D scene geometry from"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.556,
+                0.905,
+                0.603
+            ],
+            "angle": 0,
+            "content": "multiple images, we introduce a new baseline, \\(\\mathsf{RD} + \\mathsf{MoGe}\\). We include more details in the supplementary. Unless otherwise specified, all evaluations use 2-8 input images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
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+                0.71,
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+            "angle": 0,
+            "content": "4.2. Evaluation on CO3D"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.644,
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+                0.901
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+            "angle": 0,
+            "content": "Camera Pose Accuracy. We present the quantitative results in Tab. 1. For camera rotation accuracy, both versions of DiffusionSfM outperform all baselines, except that DUSt3R achieves slightly higher overall accuracy than DiffusionSfM-CO3D on unseen categories – likely due to its training on more data. For camera center accuracy, our approach consistently outperforms all other methods. We hypothesize that these gains stem from our explicit modeling of camera centers through ray origin prediction. The qualitative results in Fig. 3 illustrate that DiffusionSfM produces robust predictions given challenging inputs, whereas DUSt3R produces inaccurate results. We attribute this improvement to our model's probabilistic modeling capability derived from diffusion, as well as its multi-view reasoning abilities, which together effectively handle these challenging scenarios. While we observe that DUSt3R can predict highly precise camera rotations, it often struggles with cam-"
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\"># of Images</td><td colspan=\"6\">Rotation Accuracy (↑, @ 15°)</td><td colspan=\"7\">Center Accuracy (↑, @ 0.1)</td></tr><tr><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td></tr><tr><td rowspan=\"8\">Seen Categories</td><td>COLMAP [22]</td><td>30.7</td><td>28.4</td><td>26.5</td><td>26.8</td><td>27.0</td><td>28.1</td><td>30.6</td><td>100</td><td>34.5</td><td>23.8</td><td>18.9</td><td>15.6</td><td>14.5</td></tr><tr><td>PoseDiffusion [34]</td><td>75.7</td><td>76.4</td><td>76.8</td><td>77.4</td><td>78.0</td><td>78.7</td><td>78.8</td><td>100</td><td>77.5</td><td>69.7</td><td>65.9</td><td>63.7</td><td>62.8</td></tr><tr><td>RelPose++ [12]</td><td>81.8</td><td>82.8</td><td>84.1</td><td>84.7</td><td>84.9</td><td>85.3</td><td>85.5</td><td>100</td><td>85.0</td><td>78.0</td><td>74.2</td><td>71.9</td><td>70.3</td></tr><tr><td>RayDiffusion [41]</td><td>91.8</td><td>92.4</td><td>92.6</td><td>92.9</td><td>93.1</td><td>93.3</td><td>93.3</td><td>100</td><td>94.2</td><td>90.5</td><td>87.8</td><td>86.2</td><td>85.0</td></tr><tr><td>DUSt3R-CO3D [36]</td><td>86.7</td><td>87.9</td><td>88.0</td><td>88.2</td><td>88.6</td><td>88.8</td><td>88.9</td><td>100</td><td>92.0</td><td>86.8</td><td>83.8</td><td>82.0</td><td>81.1</td></tr><tr><td>DUSt3R [36]</td><td>91.7</td><td>92.7</td><td>93.3</td><td>93.6</td><td>93.8</td><td>94.0</td><td>94.3</td><td>100</td><td>93.0</td><td>85.7</td><td>81.9</td><td>79.6</td><td>77.8</td></tr><tr><td>DiffusionSfM-CO3D</td><td>93.4</td><td>94.0</td><td>94.5</td><td>94.8</td><td>95.0</td><td>95.2</td><td>95.1</td><td>100</td><td>95.9</td><td>93.6</td><td>92.2</td><td>91.2</td><td>90.7</td></tr><tr><td>DiffusionSfM</td><td>92.4</td><td>93.5</td><td>94.0</td><td>94.5</td><td>94.7</td><td>95.1</td><td>95.2</td><td>100</td><td>95.3</td><td>92.9</td><td>91.9</td><td>91.2</td><td>90.8</td></tr><tr><td rowspan=\"8\">Unseen Categories</td><td>COLMAP [22]</td><td>34.5</td><td>31.8</td><td>31.0</td><td>31.7</td><td>32.7</td><td>35.0</td><td>38.5</td><td>100</td><td>36.0</td><td>25.5</td><td>20.0</td><td>17.9</td><td>17.6</td></tr><tr><td>PoseDiffusion [34]</td><td>63.2</td><td>64.2</td><td>64.2</td><td>65.7</td><td>66.2</td><td>67.0</td><td>67.7</td><td>100</td><td>63.6</td><td>50.5</td><td>45.7</td><td>43.0</td><td>41.2</td></tr><tr><td>RelPose++ [12]</td><td>69.8</td><td>71.1</td><td>71.9</td><td>72.8</td><td>73.8</td><td>74.4</td><td>74.9</td><td>100</td><td>70.6</td><td>58.8</td><td>53.4</td><td>50.4</td><td>47.8</td></tr><tr><td>RayDiffusion [41]</td><td>83.5</td><td>85.6</td><td>86.3</td><td>86.9</td><td>87.2</td><td>87.5</td><td>88.1</td><td>100</td><td>87.7</td><td>81.1</td><td>77.0</td><td>74.1</td><td>72.4</td></tr><tr><td>DUSt3R-CO3D [36]</td><td>79.8</td><td>81.5</td><td>82.6</td><td>82.7</td><td>83.0</td><td>83.3</td><td>83.7</td><td>100</td><td>83.6</td><td>77.2</td><td>71.8</td><td>70.0</td><td>68.1</td></tr><tr><td>DUSt3R [36]</td><td>90.8</td><td>92.6</td><td>93.6</td><td>93.6</td><td>93.8</td><td>93.6</td><td>93.4</td><td>100</td><td>87.9</td><td>79.8</td><td>74.3</td><td>71.7</td><td>69.4</td></tr><tr><td>DiffusionSfM-CO3D</td><td>90.4</td><td>91.2</td><td>92.7</td><td>93.0</td><td>93.1</td><td>93.3</td><td>93.5</td><td>100</td><td>91.1</td><td>87.7</td><td>85.3</td><td>83.7</td><td>82.7</td></tr><tr><td>DiffusionSfM</td><td>91.5</td><td>92.8</td><td>93.6</td><td>93.9</td><td>94.1</td><td>94.2</td><td>94.4</td><td>100</td><td>92.4</td><td>87.9</td><td>86.2</td><td>85.3</td><td>84.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.371,
+                0.907,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Table 1. Camera Rotation and Center Accuracy on CO3D. On the left, we report the proportion of relative camera rotations within \\(15^{\\circ}\\) of the ground truth. On the right, we report the proportion of camera centers within \\(10\\%\\) of the scene scale, relative to the ground truth. To align the predicted camera centers to ground truth, we apply an optimal similarity transform \\((s, \\mathbf{R}, \\mathbf{t})\\), hence the alignment is perfect at \\(N = 2\\) but worsens with more images. DiffusionSfM outperforms all other methods for camera center accuracy, and outperforms all methods trained on equivalent data for rotation accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.461,
+                0.483,
+                0.492
+            ],
+            "angle": 0,
+            "content": "era centers (see the backpack example). Additional qualitative results on camera accuracy are provided in Fig.4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.093,
+                0.494,
+                0.483,
+                0.751
+            ],
+            "angle": 0,
+            "content": "Predicted Geometry. To evaluate predicted geometry, we compute Chamfer Distance (CD) and show comparisons against baselines in Tab. 2. We compute CD in two setups (with and without foreground object mask), and find that DiffusionSfM-CO3D performs best without foreground masking. In this setup, the predicted ray endpoints corresponding to the background image pixels tend to have larger coordinate values than foreground ones, and therefore dominate CD. This result indicates that our model provides more accurate predictions for complex image backgrounds. In terms of CD with masking, DUSt3R achieves the best result, while our two model variants outperform DUSt3R-CO3D. See Fig. 3 for visualization. We also notice that naively combining RayDiffusion poses with estimated depths from MoGe does not work well, as the inferred depths are potentially inconsistent across different views, thus resulting in degraded performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.77,
+                0.4,
+                0.787
+            ],
+            "angle": 0,
+            "content": "4.3. Evaluation on Scene-Level Datasets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.795,
+                0.483,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Beyond the object-centric CO3D dataset [21], we compare DiffusionSfM against DUSt3R on two scene-level datasets: Habitat (in-distribution) [24] and RealEstate10k (out-of-distribution) [42]. The results are presented in Tab. 3. While DiffusionSfM achieves comparable camera rotation accuracy to DUSt3R, it consistently predicts more accurate camera centers, aligning with our findings on CO3D."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.517,
+                0.458,
+                0.905,
+                0.635
+            ],
+            "angle": 0,
+            "content": "<table><tr><td># of Images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>RD*+MoGe [41]</td><td>0.059</td><td>0.064</td><td>0.071</td><td>0.062</td><td>0.063</td><td>0.061</td><td>0.061</td></tr><tr><td>DUSt3R* [36]</td><td>0.036</td><td>0.037</td><td>0.040</td><td>0.040</td><td>0.037</td><td>0.036</td><td>0.039</td></tr><tr><td>DUSt3R [36]</td><td>0.021</td><td>0.023</td><td>0.024</td><td>0.024</td><td>0.025</td><td>0.025</td><td>0.023</td></tr><tr><td>DiffusionSfM*</td><td>0.019</td><td>0.021</td><td>0.022</td><td>0.022</td><td>0.021</td><td>0.021</td><td>0.021</td></tr><tr><td>DiffusionSfM</td><td>0.025</td><td>0.025</td><td>0.025</td><td>0.025</td><td>0.026</td><td>0.025</td><td>0.028</td></tr><tr><td>RD*+MoGe [41]</td><td>0.071</td><td>0.075</td><td>0.068</td><td>0.067</td><td>0.066</td><td>0.064</td><td>0.064</td></tr><tr><td>DUSt3R* [36]</td><td>0.038</td><td>0.036</td><td>0.036</td><td>0.036</td><td>0.034</td><td>0.033</td><td>0.034</td></tr><tr><td>DUSt3R [36]</td><td>0.023</td><td>0.022</td><td>0.019</td><td>0.020</td><td>0.019</td><td>0.020</td><td>0.020</td></tr><tr><td>DiffusionSfM*</td><td>0.028</td><td>0.025</td><td>0.024</td><td>0.024</td><td>0.024</td><td>0.023</td><td>0.022</td></tr><tr><td>DiffusionSfM</td><td>0.027</td><td>0.024</td><td>0.023</td><td>0.022</td><td>0.022</td><td>0.022</td><td>0.021</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.513,
+                0.645,
+                0.907,
+                0.73
+            ],
+            "angle": 0,
+            "content": "Table 2. Chamfer Distance \\((\\downarrow)\\) on CO3D Unseen Categories. Top: CD computed on all scene points. Bottom: CD computed on foreground points only. Models marked with “*” are trained on CO3D only, while those without are trained on multiple datasets. Note that top and bottom values are not directly comparable, as each ground-truth point cloud is individually normalized."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.757,
+                0.673,
+                0.774
+            ],
+            "angle": 0,
+            "content": "4.4. Inference Speed"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.78,
+                0.907,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Though our method requires iterative diffusion denoising at inference, we can speed this up by performing early stopping. Specifically, we can treat the \\( x_0 \\)-prediction from early timesteps as our output instead of iterating over all denoising timesteps. Consistent with observations by Zhang et al. [41], this in fact yields more accurate predictions than the final-step diffusion outputs. As a result we only require 10 denoising diffusion timesteps for inference, taking 1.91"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6323"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.095,
+                0.089,
+                0.48,
+                0.155
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Hab.</td><td>DUSt3R</td><td>97.0/100</td><td>95.0/97.6</td><td>94.3/95.0</td><td>94.2/93.1</td></tr><tr><td>DiffusionSfM</td><td>92.6/100</td><td>93.7/99.1</td><td>94.2/98.8</td><td>94.9/98.6</td></tr><tr><td rowspan=\"2\">RE10</td><td>DUSt3R</td><td>98.1/100</td><td>97.7/68.7</td><td>97.6/57.9</td><td>97.7/53.3</td></tr><tr><td>DiffusionSfM</td><td>97.8/100</td><td>97.5/75.6</td><td>97.7/66.2</td><td>97.9/61.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.164,
+                0.483,
+                0.248
+            ],
+            "angle": 0,
+            "content": "Table 3. Camera Rotation and Center Accuracy on Two Scene-Level Datasets. Top: Habitat (2-5 views). Bottom: RealEstate10k (2, 4, 6, 8 views). Each grid reports camera rotation accuracy (left, \\(\\uparrow\\)) and center accuracy (right, \\(\\uparrow\\)). While DiffusionSfM performs on par with DUSt3R in rotation accuracy, it consistently surpasses DUSt3R in center accuracy."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.093,
+                0.266,
+                0.483,
+                0.325
+            ],
+            "angle": 0,
+            "content": "<table><tr><td># of Images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>DiffusionSfM*</td><td>0.019</td><td>0.021</td><td>0.022</td><td>0.022</td><td>0.021</td><td>0.021</td><td>0.021</td></tr><tr><td>w/o Mask</td><td>0.020</td><td>0.022</td><td>0.023</td><td>0.023</td><td>0.022</td><td>0.022</td><td>0.024</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.335,
+                0.483,
+                0.42
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation Study on GT Mask Conditioning for CO3D Unseen Categories. We assess the effect of replacing GT mask conditioning with depth interpolation in our CO3D variant (DiffusionSfM*), by reporting the CD for predicted geometry. Incorporating mask conditioning to indicate missing data during training improves geometry quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.451,
+                0.484,
+                0.512
+            ],
+            "angle": 0,
+            "content": "seconds on a single A5000 GPU with 8 input images. In contrast, DUSt3R takes 8.73 seconds to run the complete pairwise inference and global alignment procedure. We provide additional analysis in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.527,
+                0.245,
+                0.543
+            ],
+            "angle": 0,
+            "content": "4.5. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.551,
+                0.483,
+                0.657
+            ],
+            "angle": 0,
+            "content": "Homogeneous Coordinates. The use of homogeneous coordinates for ray origins and endpoints is crucial for stable model training. To assess its impact, we replace the proposed homogeneous representation with standard 3D coordinates in \\(\\mathbb{R}^3\\). Our experiments show that this variant is difficult to train and fails to converge. Further details on this experiment are provided in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.659,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "GT Mask Conditioning. To evaluate the effectiveness of the proposed GT mask conditioning, we train a baseline model without using this strategy. For missing values in the ground-truth depth maps, we use nearest-neighbor interpolation to fill in invalid pixels. This experiment is conducted on the CO3D dataset, with results presented in Tab. 4. The findings show that removing GT mask conditioning consistently degrades predicted geometry across varying numbers of input views, even when the loss is still masked. While interpolation can effectively fill missing depth within object regions, it often introduces substantial noise in the background (e.g., the sky). This noise negatively impacts diffusion model training, as the entire ray origin and endpoint maps are used as input. We anticipate an even larger performance gap on non-object-centric datasets with more outdoor scenes, such as MegaDepth [11]."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.517,
+                0.088,
+                0.909,
+                0.18
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.512,
+                0.189,
+                0.907,
+                0.287
+            ],
+            "angle": 0,
+            "content": "Figure 5. Multi-modality of DiffusionSfM. We show two distinct samples from DiffusionSfM, starting from the same input images but with different random noise. Sample 1 explains the input images by putting all flowers on the left side, while Sample 2 places one flower on each side (note the difference in the green camera's viewpoint). DiffusionSfM is able to predict multi-modal geometry distributions when the scene layout is ambiguous in the inputs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.313,
+                0.857,
+                0.33
+            ],
+            "angle": 0,
+            "content": "4.6. Multi-modality from Multiple Sampling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.335,
+                0.907,
+                0.472
+            ],
+            "angle": 0,
+            "content": "Diffusion models enable the generation of diverse samples from challenging input images. For instance, in Fig. 5, the vase exhibits symmetric patterns, and we present two distinct predicted endpoints from DiffusionSfM, each offering a different interpretation of the flowers in the image. Compared to regression models such as DUSt3R [8], DiffusionSfM is better suited for handling uncertainty – an inherent aspect of our task – where a sparse set of input images can correspond to multiple plausible 3D scene geometry."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.484,
+                0.628,
+                0.5
+            ],
+            "angle": 0,
+            "content": "5. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.51,
+                0.906,
+                0.57
+            ],
+            "angle": 0,
+            "content": "We present DiffusionSfM and demonstrate that it recovers accurate predictions of both cameras and geometry from multi-view inputs. Although our results are promising, several challenges and open questions remain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.57,
+                0.906,
+                0.751
+            ],
+            "angle": 0,
+            "content": "Notably, DiffusionSfM employs a pixel-space diffusion model, in contrast to the latent-space models adopted by state-of-the-art T2I generative systems. Operating in pixel space may require greater model capacity, yet our current model remains relatively small - potentially explaining the noisy patterns observed along object boundaries. Learning an expressive latent space for ray origins and endpoints by training a VAE could be a promising direction for future work. In addition, the compute requirement in multi-view transformers scales quadratically with the number of input images: one would require masked attention to deploy systems like ours for a large set of input images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.751,
+                0.909,
+                0.888
+            ],
+            "angle": 0,
+            "content": "Despite these challenges, we believe that our work highlights the potential of a unified approach for multi-view geometry tasks. We envision that our approach can be built upon to train a common system across related geometric tasks, such as SfM (input images with unknown origins and endpoints), registration (some images have known origins and endpoints, whereas others don't), mapping (known rays but unknown endpoints), and view synthesis (unknown pixel values for known rays)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6324"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.482,
+                0.151
+            ],
+            "angle": 0,
+            "content": "Acknowledgements: We thank the members of the Physical Perception Lab at CMU for their valuable discussions, and extend special thanks to Yanbo Xu for his insights on diffusion models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.153,
+                0.483,
+                0.394
+            ],
+            "angle": 0,
+            "content": "This work used Bridges-2 [4] at Pittsburgh Supercomputing Center through allocation CIS240166 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296. This work was supported by Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.093,
+                0.405,
+                0.188,
+                0.42
+            ],
+            "angle": 0,
+            "content": "References"
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+        {
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+            ],
+            "angle": 0,
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2025/DiffusionSfM_ Predicting Structure and Motion via Ray Origin and Endpoint Diffusion/a0e804a0-3c59-43c5-bb05-b2160d8636bd_origin.pdf

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2025/DiffusionSfM_ Predicting Structure and Motion via Ray Origin and Endpoint Diffusion/full.md

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+# DiffusionSfM: Predicting Structure and Motion via Ray Origin and Endpoint Diffusion
+
+Qitao Zhao, Amy Lin, Jeff Tan, Jason Y. Zhang, Deva Ramanan, Shubham Tulsiani Carnegie Mellon University
+
+Project page: qitaozhao.github.io/DiffusionSfM
+
+![](images/ac31d7718dc556e701eba8b776c1f3e30bb00ad6f957b560bb72e53affc2382c.jpg)  
+Figure 1. DiffusionSfM. Top: Given a set of multi-view images (left), DiffusionSfM represents scene geometry and cameras (right) as pixel-wise ray origins and endpoints in a global frame. It learns a denoising diffusion model to infer these elements directly from multiview inputs. Unlike traditional Structure-from-Motion (SfM) pipelines, which separate pairwise reasoning and global optimization into two stages, our approach unifies both into a single end-to-end multi-view reasoning framework. Bottom: Example results of inferred scene geometry and cameras for two distinct settings: a real-world outdoor scene (left) and a synthetic indoor scene (right).
+
+# Abstract
+
+Current Structure-from-Motion (SfM) methods typically follow a two-stage pipeline, combining learned or geometric pairwise reasoning with a subsequent global optimization step. In contrast, we propose a data-driven multi-view reasoning approach that directly infers 3D scene geometry and camera poses from multi-view images. Our framework, DiffusionSfM, parameterizes scene geometry and cameras as pixel-wise ray origins and endpoints in a global frame and employs a transformer-based denoising diffusion model to predict them from multi-view inputs. To address practical challenges in training diffusion models with missing data and unbounded scene coordinates, we introduce specialized mechanisms that ensure robust learning. We empirically validate DiffusionSfM on both synthetic and real datasets, demonstrating that it outperforms classical and learning-based approaches while naturally modeling uncertainty.
+
+# 1. Introduction
+
+The task of recovering structure (geometry) and motion (cameras) from multi-view images has long been a focus of the computer vision community, with typical pipelines [25] performing pairwise correspondence estimation followed by global optimization. While classical methods relied on hand-designed features, matching, and optimization, there has been a recent shift towards incorporating learning-based alternatives [5, 6, 14, 23]. More recently, the widely influential DUSt3R [36] advocates for predicting pairwise 3D pointmaps (instead of only correspondences), demonstrating that this can yield accurate dense geometry and cameras. In order to reconstruct more than two views, DUSt3R (and its variants [10]) still require a global optimization reminiscent of classic bundle adjustment. While these methods, both classical and learning-based, have led to impressive improvements in SfM, the overall approach is largely unchanged – learned or geometric pairwise reasoning followed by global optimization. In this work, we
+
+seek to develop an alternative approach that directly predicts both structure and motion, unifying pairwise reasoning and global optimization into a single multi-view framework.
+
+We are of course not the first to attempt to find unified alternatives to the two-stage SfM pipeline. In the sparse-view setting where conventional correspondence-based methods struggle, several works employ multi-view architectures to jointly reason across input images. SparsePose [26], RelPose++ [12], and PoseDiffusion [34] all leverage multiview transformers to estimate camera pose for input images, albeit using differing mechanisms such as regression, energy-based modeling, and denoising diffusion. More recently, RayDiffusion [41] argues for a local raymap parameterization of cameras instead of a global extrinsic matrix and shows that existing patch-based transformers can be easily adapted for this task, yielding significantly more accurate pose predictions. Importantly, such methods predict only camera motion and fail to predict scene structure.
+
+In this work, we present DiffusionSfM, an end-to-end multi-view model that directly infers dense 3D geometry and cameras from multiple input images. Instead of inferring (depth-agnostic) rays per image patch (as in RayDiffusion [41]) or 3D points per pixel (as in DUSt3R [36]), DiffusionSfM effectively combines both to predict ray origins and endpoints per pixel, directly reporting both scene geometry (endpoints) and generalized cameras (rays). These can readily be converted back to traditional cameras [41]. Compared to RayDiffusion, our model directly predicts structure as well as motion at a finer scale (pixel-wise v.s. patchwise). Compared to DUSt3R, our model directly predicts motion as well as structure but, even more importantly, does so for  $N$  views, eliminating the need for memory-intensive global alignment. To model uncertainty, we train a denoising diffusion model but find two key challenges that need to be addressed. First, diffusion models require (noisy) ground truth as input for training, but existing real datasets do not have known endpoints for all pixels due to missing depth in multi-view stereo. Second, the 3D coordinates of endpoints can be potentially unbounded, whereas diffusion models require normalized data. We develop mechanisms to overcome these challenges, leveraging additional "GT mask conditioning" as input to inform the model of missing input data and parameterizing 3D points in projective space instead of Euclidean space. We find these strategies allow us to learn accurate predictions for structure and motion.
+
+We train and evaluate DiffusionSfM on real-world and synthetic datasets [21, 24, 42] and find that it can infer accurate geometry and cameras for both object-centric and scene-level images (see Fig. 1). In particular, we find that DiffusionSfM yields more accurate camera estimates compared to prior work across these settings while also modeling the underlying uncertainty via the diffusion process. In summary, we show that DiffusionSfM can serve as a unified
+
+multi-view reasoning model for 3D geometry and cameras.
+
+# 2. Related Work
+
+Structure from Motion. Structure-from-Motion (SfM) systems [25] aim to simultaneously recover geometry and cameras given a set of input images. The typical SfM pipeline extracts pixel correspondences from keypoint matching [2, 16], and performs global bundle adjustment (BA) to optimize sparse 3D points and camera parameters by minimizing reprojection errors. Recently, SfM pipelines have been substantially enhanced by replacing classical subcomponents with learning-based methods, such as neural feature descriptors [6, 8], keypoint matching [15, 23, 30], and bundle adjustment [13, 32].
+
+More recently, an emerging body of research aims to unify the various SfM subcomponents into an end-to-end neural framework. Notably, ACEZero [3] fits a single neural network to input images and learns pixel-aligned 3D coordinates in a self-supervised manner, while FlowMap [27] predicts per-frame cameras and depth maps using off-the-shelf optical flow as supervision. Though ACEZero and FlowMap are promising attempts to revolutionize SfM pipelines, they both register images incrementally and may suffer under large viewpoint changes. DUSt3R [36] directly regresses 3D pointmaps from image pairs and shows strong generalization ability [11, 21]. Building on DUSt3R, MASt3R [10] introduces a feature head, offering pixel-matching capabilities. MASt3R-SfM [7] is a more scalable SfM pipeline based on MASt3R. While these approaches [7, 10, 36] show impressive performance and robustness under sparse views, they are essentially pair-based, requiring sophisticated global alignment procedures to form a consistent estimate for more than two views.
+
+Pose Estimation with Global Reasoning. For the task of sparse-view pose estimation, learning-based methods equipped with global reasoning show favorable robustness where traditional SfM methods [25, 28] fail. This line of research includes energy-based [12, 40], regression-based [26], and diffusion-based pose estimators [34, 41]. Among them, diffusion-based methods show a better ability to handle uncertainty [41]. Closest to our work, RayDiffusion [41] leverages a denoising diffusion model [9, 19] with a patch-aligned (depth-unaware) ray representation to predict generic cameras. Our method goes further and pursues a generic representation for both geometry and cameras in the form of ray origins and endpoints for each pixel. In addition to resulting in a richer output, this joint geometry and pose prediction also yields improvements for pose estimation.
+
+# 3. Method
+
+Given a set of sparse (i.e., 2-8) input images, DiffusionSfM predicts the geometry and cameras of a 3D scene in a global
+
+![](images/e313265c3ef039eaa8c98aab188fac7c1ec90a35c2ae39191b416a12c793c328.jpg)  
+Figure 2. Method. Given sparse multi-view images as input, DiffusionSfM predicts pixel-wise ray origins and endpoints in a global frame (Sec. 3.1) using a denoising diffusion process (Sec. 3.2). For each image, we compute patch-wise embeddings with DINOv2 [18] and embed noisy ray origins and endpoints into latents using a single downsampling convolutional layer, ensuring alignment with the spatial footprint of the image embeddings. We implement a Diffusion Transformer architecture that predicts clean ray origins and endpoints from noisy samples. A convolutional DPT [20] head outputs full-resolution denoised ray origins and endpoints. To handle incomplete ground truth (GT) during training, we condition the model on a GT mask (Sec. 3.3). At inference, the GT mask is set to all ones, enabling the model to predict origins and endpoints for all pixels. The predicted ray origins and endpoints can be directly visualized in 3D or postprocessed to recover camera extrinsics, intrinsics, and multi-view consistent depth maps.
+
+coordinate frame. In Sec. 3.1, we propose to represent 3D scenes as dense pixel-aligned ray origins and endpoints. To predict such scene representations from sparse input images while modeling uncertainty, Sec. 3.2 proposes a denoising diffusion architecture. We then discuss some key practical challenges in training such a model in Sec. 3.3.
+
+# 3.1. 3D Scenes as Ray Origins and Endpoints
+
+Given an input image  $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$  with a depth map  $\mathbf{D} \in \mathbb{R}^{H \times W}$ , camera intrinsics  $\mathbf{K} \in \mathbb{R}^{3 \times 3}$ , and world-to-camera extrinsics  $\mathbf{T} \in \mathbb{R}^{4 \times 4}$  (equivalently, rotation  $\mathbf{R} \in SO(3)$  and translation  $\mathbf{t} \in \mathbb{R}^3$ ), each 2D image pixel  $\mathbf{P}_{ij} = [u, v]$  corresponds to a ray that travels from the camera center  $\mathbf{c}$  through the pixel's projected position on the image plane, terminating at the object's surface as specified by the depth map  $\mathbf{D}$ . The endpoint of the ray associated with image pixel  $\mathbf{P}_{ij}$  is given by:
+
+$$
+\mathbf {E} _ {i j} = \mathbf {T} ^ {- 1} h (\mathbf {D} _ {i j} \cdot \mathbf {K} ^ {- 1} [ u, v, 1 ] ^ {T}) \tag {1}
+$$
+
+where  $h$  maps the 3D point into homogeneous coordinates. The shared ray origin  $\mathbf{O}_{ij}$  for all pixels is equivalent to the camera center  $\mathbf{c}$ , and can be computed as:
+
+$$
+\mathbf {O} _ {i j} = \mathbf {c} = h (- \mathbf {R} ^ {- 1} \mathbf {t}) \tag {2}
+$$
+
+In summary, we associate each image pixel with a ray origin and endpoint  $\mathbf{S}_{ij} = \langle \mathbf{O}_{ij},\mathbf{E}_{ij}\rangle$  in world coordinates, describing the location of the observing camera and the observed 3D point on the object surface. Given a bundle of ray origins and endpoints, we can easily extract the corresponding camera pose [41].
+
+Learning Over-Parameterized Representations. We represent 3D scenes and cameras using distributed ray origins  $\mathbf{O}$  and endpoints  $\mathbf{E}$  rather than global alternatives such as quaternions and translation vectors. This design is inspired by RayDiffusion [41], and it facilitates the use of the
+
+distributed deep features learned by state-of-the-art vision backbones, such as DINOv2 [18], which encode image information in a patch-wise manner. Notably, while ray origins  $\mathbf{O}$  should ideally be identical across all pixels, we predict them densely alongside ray endpoints  $\mathbf{E}$ . This encourages ray origins to remain close within the same image, providing implicit regularization during training. Practically, predicting both ray origins and endpoints simultaneously is easy to implement using a single projection head.
+
+# 3.2. DiffusionSfM
+
+We propose a denoising Diffusion Transformer (DiT) architecture [19] that predicts ray origins and endpoints (Sec. 3.1) via a denoising diffusion process. An overview of DiffusionSfM is given in Fig. 2.
+
+Diffusion Framework. Given pixel-aligned ray origins and endpoints  $S = \text{stack}(\{\mathbf{S}^{(n)}\}_{n=1}^{N})$  associated with a set of  $N$  input images, we apply a forward diffusion process [9, 29] that adds time-dependent Gaussian noise to them. Let  $S_{t}$  denote the noisy ray origins and endpoints at timestep  $t$ , where  $S_{0}$  is the clean sample and  $S_{T}$  (at the final diffusion step  $T$ ) approximates pure Gaussian noise. The forward diffusion process is defined as:
+
+$$
+\mathcal {S} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathcal {S} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon \tag {3}
+$$
+
+where  $t \sim \mathrm{Uniform}(0, T]$ ,  $\epsilon \sim \mathcal{N}(0, I)$ , and  $\bar{\alpha}_t$  follows a pre-defined noise schedule that controls the strength of added noise at each timestep. To perform the reverse diffusion process, which progressively reconstructs the clean sample given noisy observations, we train a diffusion model  $f_\theta$  that takes  $\mathcal{S}_t$  as input and optionally incorporates additional conditioning information  $\mathcal{C}$ . The model is trained using the following loss function (with the "  $x_0$ " objective):
+
+$$
+\mathcal {L} _ {\text {D i f f u s i o n}} = \mathbb {E} _ {t, S _ {0}, \epsilon} \| S _ {0} - f _ {\theta} (S _ {t}, t, \mathcal {C}) \| ^ {2} \tag {4}
+$$
+
+Architecture. We implement  $f_{\theta}$  using a DiT [19] architecture conditioned on deep image features  $\mathcal{C} \in \mathbb{R}^{N \times h \times w \times c_1}$  from DINOv2 [18], where  $h$  and  $w$  are the patch resolution and  $c_1$  is the embedding dimension. To align pixels to the spatial information learned by DINOv2, we apply a convolutional layer with kernel size and stride equal to ViT patch size: this spatially downsamples the noisy ray origins and endpoints  $S_t$  to match the DINOv2 features while increasing their feature dimension:
+
+$$
+\mathcal {F} = \operatorname {C o n v} \left(\mathcal {S} _ {t}\right) \in \mathbb {R} ^ {N \times h \times w \times c _ {2}} \tag {5}
+$$
+
+The combined DiT input is constructed by concatenating these two feature sets along the channel dimension:  $\mathcal{F} \oplus \mathcal{C}$ . Within DiT, patch-wise features attend to others through self-attention [33]. To distinguish between different images and their respective patches, we apply sinusoidal positional encoding [33] based on image and patch indices.
+
+While the DiT operates on low-resolution features, our objective is to produce pixel-aligned dense ray origins and endpoints. To achieve this, we employ a DPT (Dense Prediction Transformer) [20] decoder, which takes intermediate feature maps from both DINoV2 and DiT as inputs. The DPT decoder progressively increases the feature resolution through several convolutional layers. The final ray origins and endpoints are decoded from the DPT output using a single linear layer. During inference, we apply the trained model in the reverse diffusion process to iteratively denoise a randomly initialized Gaussian sample.
+
+# 3.3. Practical Training Considerations
+
+Homogeneous Coordinates for Unbounded Geometry. Real-world scenes often exhibit significant variations in scale, both across different scenes and within a single scene. While normalizing by the average distance of 3D points [36] helps address cross-scene variation, within-scene variations remain. For instance, a background building may be much farther away than foreground elements, potentially resulting in extremely large coordinate values when generating ground-truth ray origins and endpoints. However, neural networks (especially diffusion models) tend to train most effectively when working with bounded inputs and outputs (e.g., between -1 and 1). To stabilize training across the large scale variations present in 3D scene datasets, we propose to represent ray origins and endpoints in homogeneous coordinates. Specifically, given any 3D point, we apply a homogeneous transform from  $\mathbb{R}^3\to \mathbb{P}^3$ :
+
+$$
+(x, y, z) \rightarrow \frac {1}{w} (x, y, z, 1) \tag {6}
+$$
+
+where  $w$  is an arbitrary scale factor. To encourage bounded coordinates in practice, we choose  $w$  such that the homogeneous coordinate is unit-norm:
+
+$$
+w := \sqrt {x ^ {2} + y ^ {2} + z ^ {2} + 1} \tag {7}
+$$
+
+Unit normalization allows homogeneous coordinates to serve as a bounded representation for unbounded scene geometry. For example,  $(x,y,z,0)$  is a point at infinity in the direction of  $(x,y,z)$ . We find that this representation makes large coordinate values more tractable during training.
+
+Training with Incomplete Ground Truth. Many real-world datasets (e.g., CO3D [21] and MegaDepth [11]), provide only sparse point clouds, leading to incomplete depth information. This presents a significant challenge in diffusion training, as ground-truth (GT) depth values that are used to create clean ray endpoints often contain invalid or missing data. It is highly undesirable for these missing ray endpoints to be interpreted as part of the target distribution. Unlike regression models (e.g., DUSt3R [36]), which do not require (noisy) GT data as input and can simply apply a mask on the loss for supervision, diffusion models must handle incomplete inputs during training.
+
+To mitigate this issue, we further apply GT masks  $\mathcal{M} \in \mathbb{R}^{N \times H \times W}$  to the DiT inputs, where zero values indicate pixels with invalid depth. During training, we multiply DiT inputs with GT masks element-wise, then concatenate along the channel dimension:  $S_{t}' = (\mathcal{M} \cdot S_{t}) \oplus \mathcal{M}$ . Then, we only compute the diffusion loss in Eq. 4 over unmasked pixels. By implementing these strategies, we encourage the model to focus on regions with valid GT values during training. During inference, however, we would like the diffusion process to estimate ray endpoints at all pixels, so we always use GT masks with values set to one.
+
+Sparse-to-Dense Training. In practice, we find that training the entire model from scratch leads to slow convergence and suboptimal performance. To address this, we propose a sparse-to-dense training approach. First, we train a sparse version of the model, where the DPT decoder is removed, and the output ray origins and endpoints have the same spatial resolution as the DINOv2 features. Unlike Eq. 5, no spatial downsampling is required, so this sparse model uses a single linear layer to embed the noisy ray origins and endpoints. Once the sparse model is trained, we initialize the dense model DiT with the learned weights from the sparse model. This two-stage approach significantly improves performance; see the supplementary material for comparisons.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. We introduce two model variants, each trained on different datasets. (1) DiffusionSfM-CO3D: Following prior work [12, 41], we train and evaluate our model on the CO3D dataset [21], which consists of turntable video sequences of various object categories. Specifically, we train on 41 object categories and evaluate on both these seen categories and an additional 10 unseen categories to assess generalization. (2) DiffusionSfM: This variant is trained on the
+
+![](images/d6e463bb54fb1e9753a107c4e0f00652fabfafb5aeb6a00a0e8c75bcf8a0d463.jpg)  
+Input Images /GT Point Clouds
+
+![](images/dc5f60efbcfe9c7755289675788486c4578c9f213d2b6042429e3e03c31ae41f.jpg)
+
+![](images/4a90c02cbf86ede1c3b9f9128f7369efafe2004fac7f244144acbef7b880efc4.jpg)  
+DiffusionSfM
+
+![](images/4dbeed7353c79ac7b9a429bdb597e8c4bf321a4dea76408dad8d2d25a4cb3311.jpg)  
+RD + MoGe
+
+![](images/3c4d4f0156271974c5a1bea2211d4c0da5b8a04dce2f24b68c677ecb90c28e64.jpg)  
+DUSt3R
+
+![](images/08b9d18a8fd24f92149aabec1779e2696ba49c6f961ae07dcdb2a0eb2a56a1d2.jpg)
+
+![](images/6d07fe01df1484bab4bf2ec9045876531d07cc800c093177a7bbbbbfac0de292.jpg)
+
+![](images/21cddbbf7d3c3a2aa6c186d5790bb68351b7e18e5fec658f160d0f440c0ebba2.jpg)
+
+![](images/4467112fd81e570e98956508a4e57480691fb0ba442c38bbf2627e053ef2ac55.jpg)
+
+![](images/272dd89e3cebb5972006b1e754848a814b96b262781b027efbac94167d73da4f.jpg)
+
+![](images/f9d752bc2a72574ad8da4962e3c75c5038c52407176760b4817e89875dc60734.jpg)
+
+![](images/77e3edccd4250d49af8e4e40afe6cba4c9d6793ae40e2556aa588e44db248cf8.jpg)
+
+![](images/764b33e09ba83273a035143014a202821327b88eae6f527e802b136b7abbff21.jpg)
+
+![](images/abec2e30ad827dfb18d995acedef81d339f0eae11fb77e60e29a29e8e3f6f10d.jpg)
+
+![](images/083a0c1897454b692a6d69688d3baf77dee68c4161fa70f086982461b4a28fe5.jpg)
+
+![](images/15555cfb9f16f6fdc453589fc0c91b42a2258d1260a60ff53f08904d6c5ffc59.jpg)
+
+![](images/d9ba0182fe76e9bcf638276fbe614ef41034a2b339947df162dd809ad1cd3fa0.jpg)
+
+![](images/42ead853a68a77308aba6a032385977d1aee9b389b6819fe8f30cd69f3b1bd53.jpg)
+
+![](images/3d56dfda9c0cd215776b017ae9736d19c24d055bcab58416313922bee5a94489.jpg)
+
+![](images/b1b3bbe97ed1d5d38efbfd8c6a271fd8662c88298f9063cb5d973f46e0ab718e.jpg)
+
+![](images/c44111bf71e33372cf04e561079591ede87ef0cb656da94d7fb85cf5cd0f6dba.jpg)
+
+![](images/621af54fe4b9ca0aa56cb232e2c29f811110ddb5e15082e17e506a654080d459.jpg)
+
+![](images/75308784803a2b539f04991f58dc5590242f78993005180f68724760b4e2d4f9.jpg)
+
+![](images/8ff9e2401bc30c177a123e84029058340270d40a3e6b1993cc4d906e2ce533e5.jpg)
+
+![](images/64b87ce018823ad58c1359ca2b1ff31994f93d3890ad8717504cbb3578ac1657.jpg)
+
+![](images/c919abb7dcae4e0ccf25434d3735e9779fcdd4eeae41a41a769f2dbcea89668c.jpg)
+
+![](images/a9ea49154a5cddebf7b1215c95540c58c714ca3a87f5f9090d30a8f5a9a5356c.jpg)  
+Figure 3. Qualitative Comparison on Camera Pose Accuracy and Predicted Geometry. For each method, we plot the ground-truth cameras in black and the predicted cameras in other colors. DiffusionSfM demonstrates robust performance even with challenging inputs. Compared to DUSt3R, which sometimes fails to register images in a consistent manner, DiffusionSfM consistently yields a coherent global prediction. Additionally, while we observe that DUSt3R can predict highly precise camera rotations, it often struggles with camera centers (see the backpack example). Input images depicting scenes are out-of-distribution for RayDiffusion, as it is trained on CO3D only.
+
+![](images/1737d179f0ff07dcf799bb9ca29f91d33c878cd8e84667b551b4f902f45aa969.jpg)
+
+![](images/b07132582448c16a63a6b68ee425225bc70df6e576c168687035e4f1ffa818fa.jpg)
+
+![](images/355211bdc5d80708987da0be50e094a64357cea1d97bc362e30bbd5e8f491890.jpg)
+
+![](images/052155bee2775d35833066115b297323f753cce3a22d8fe57f655f5794fe4c81.jpg)
+
+![](images/9e2d0801addb462fc02b573b35ec15afd43788406b3ddcbf55c1a5652275a7ab.jpg)
+
+![](images/95779d7f8c4d99450912c29e23c3a409997915c022968df709dfd3b6abb7c648.jpg)
+
+datasets used for DUSt3R [36], excluding Waymo [31] due to its excessively sparse depth maps. The included datasets are Habitat [24], CO3D [21], ScanNet++ [39], ArkitScenes [1], Static Scenes 3D [17], MegaDepth [11], and BlendedMVS [38]. We follow the DUSt3R official repository [37]
+
+guidelines to extract image pairs, ensuring reasonable overlap between paired images. To construct multi-view data given these pre-computed pairs, we iteratively sample images using an adjacency matrix, maintaining sufficient overlap with the selected set. Beyond CO3D, this model variant
+
+![](images/8113542d26e8415e7fccb43a4ab137fe288e9ddfb3159e473e2445238d6cf63d.jpg)  
+Input Images
+
+![](images/933b09eb7e3527150f3be3f259b770ea88c020ef8b967f7a83a4d6eafe070ecc.jpg)  
+DiffusionSfM
+
+![](images/ebb549fcdbcce39636c90442061595ecb9be761d0dac36f498c4259fa3e9299b.jpg)  
+RayDiffusion
+
+![](images/3d9b95e9ad7374161e5cbf61c41771e2e6b56aedb7c1c0789d6480c724ed3950.jpg)  
+DUSt3R
+
+![](images/c9e3727a7835cb21302b9686d7fc17c3b5fa3dc25d6a1046592ee7a962cf2cad.jpg)
+
+![](images/3ba083c2b95cf328bae57df050f1ef358611952760041f8e249fa443105d4deb.jpg)
+
+![](images/391548a854ffbf9d9e3b6c9a89f4c7f4a8c2303a99b0f5684284a04001ea7fd6.jpg)
+
+![](images/71982fd3c12d0817f39efa883fc6e901683dd4fcb9958618f0e0e0c14e24d0ec.jpg)
+
+![](images/01f965a7ac2be332782e20e3ebbaef854eed14bc732b6658975749ecb53a0bb9.jpg)
+
+![](images/3a0473971df79c5449389de83b9765f9583258dd642a4923b3125fc4447d8398.jpg)
+
+![](images/fc70de8b11828fc1a07930f61b93d9c100c1903b7fb41fcd5d39ea6065293654.jpg)
+
+![](images/e62c7dc2190fad5f4b7bdae298e3183cc133b3b08212eed26461b84525924ed5.jpg)
+
+![](images/12bc1a5e9df8ccb453a2c73ad7e51bab942f03cf2f0f7966ec16278b98e03951.jpg)  
+Figure 4. Additional Qualitative Results on Predicted Camera Poses. DiffusionSfM shows robustness to ambiguous patterns in inputs.
+
+![](images/43d9c1f6b2fb34cfb80eb04d4a1eace850a5c28b1428f2923e0531d60d3fcbfe.jpg)
+
+![](images/0fb6fb31f2c126f48b00a94419cbada66bd471bb4696337619753970c8eb7ed5.jpg)
+
+is also evaluated on Habitat and RealEstate10k [42].
+
+Baselines and Metrics. To evaluate camera pose accuracy in the sparse-view setup, we compare with RayDiffusion [41] and DUSt3R [36], along with previous methods [12, 22, 34]. DUSt3R is trained initially on a mixture of eight datasets, while most other baselines are trained only on CO3D. For a fair and comprehensive comparison, we re-train DUSt3R on the 41-10 split of CO3D, using the authors' official implementation [37] and hyperparameters (referred to as DUSt3R-CO3D). To evaluate camera predictions, we follow prior work [41] and convert predicted rays back to traditional extrinsic matrices and report two pose accuracy metrics: (1) Camera Rotation Accuracy which compares the predicted relative camera rotation between images against ground truth and (2) Camera Center Accuracy which compares predicted camera centers to the ground truth after a similarity alignment. To evaluate the estimated geometry (i.e., ray endpoints), we report Chamfer Distance (CD). Additionally, to explore whether combining an off-the-shelf sparse-view pose estimation method (RayDiffusion) with a monocular depth estimation model (MoGe [35]) is sufficient to infer 3D scene geometry from
+
+multiple images, we introduce a new baseline,  $\mathsf{RD} + \mathsf{MoGe}$ . We include more details in the supplementary. Unless otherwise specified, all evaluations use 2-8 input images.
+
+# 4.2. Evaluation on CO3D
+
+Camera Pose Accuracy. We present the quantitative results in Tab. 1. For camera rotation accuracy, both versions of DiffusionSfM outperform all baselines, except that DUSt3R achieves slightly higher overall accuracy than DiffusionSfM-CO3D on unseen categories – likely due to its training on more data. For camera center accuracy, our approach consistently outperforms all other methods. We hypothesize that these gains stem from our explicit modeling of camera centers through ray origin prediction. The qualitative results in Fig. 3 illustrate that DiffusionSfM produces robust predictions given challenging inputs, whereas DUSt3R produces inaccurate results. We attribute this improvement to our model's probabilistic modeling capability derived from diffusion, as well as its multi-view reasoning abilities, which together effectively handle these challenging scenarios. While we observe that DUSt3R can predict highly precise camera rotations, it often struggles with cam-
+
+<table><tr><td rowspan="2"></td><td rowspan="2"># of Images</td><td colspan="6">Rotation Accuracy (↑, @ 15°)</td><td colspan="7">Center Accuracy (↑, @ 0.1)</td></tr><tr><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td></tr><tr><td rowspan="8">Seen Categories</td><td>COLMAP [22]</td><td>30.7</td><td>28.4</td><td>26.5</td><td>26.8</td><td>27.0</td><td>28.1</td><td>30.6</td><td>100</td><td>34.5</td><td>23.8</td><td>18.9</td><td>15.6</td><td>14.5</td></tr><tr><td>PoseDiffusion [34]</td><td>75.7</td><td>76.4</td><td>76.8</td><td>77.4</td><td>78.0</td><td>78.7</td><td>78.8</td><td>100</td><td>77.5</td><td>69.7</td><td>65.9</td><td>63.7</td><td>62.8</td></tr><tr><td>RelPose++ [12]</td><td>81.8</td><td>82.8</td><td>84.1</td><td>84.7</td><td>84.9</td><td>85.3</td><td>85.5</td><td>100</td><td>85.0</td><td>78.0</td><td>74.2</td><td>71.9</td><td>70.3</td></tr><tr><td>RayDiffusion [41]</td><td>91.8</td><td>92.4</td><td>92.6</td><td>92.9</td><td>93.1</td><td>93.3</td><td>93.3</td><td>100</td><td>94.2</td><td>90.5</td><td>87.8</td><td>86.2</td><td>85.0</td></tr><tr><td>DUSt3R-CO3D [36]</td><td>86.7</td><td>87.9</td><td>88.0</td><td>88.2</td><td>88.6</td><td>88.8</td><td>88.9</td><td>100</td><td>92.0</td><td>86.8</td><td>83.8</td><td>82.0</td><td>81.1</td></tr><tr><td>DUSt3R [36]</td><td>91.7</td><td>92.7</td><td>93.3</td><td>93.6</td><td>93.8</td><td>94.0</td><td>94.3</td><td>100</td><td>93.0</td><td>85.7</td><td>81.9</td><td>79.6</td><td>77.8</td></tr><tr><td>DiffusionSfM-CO3D</td><td>93.4</td><td>94.0</td><td>94.5</td><td>94.8</td><td>95.0</td><td>95.2</td><td>95.1</td><td>100</td><td>95.9</td><td>93.6</td><td>92.2</td><td>91.2</td><td>90.7</td></tr><tr><td>DiffusionSfM</td><td>92.4</td><td>93.5</td><td>94.0</td><td>94.5</td><td>94.7</td><td>95.1</td><td>95.2</td><td>100</td><td>95.3</td><td>92.9</td><td>91.9</td><td>91.2</td><td>90.8</td></tr><tr><td rowspan="8">Unseen Categories</td><td>COLMAP [22]</td><td>34.5</td><td>31.8</td><td>31.0</td><td>31.7</td><td>32.7</td><td>35.0</td><td>38.5</td><td>100</td><td>36.0</td><td>25.5</td><td>20.0</td><td>17.9</td><td>17.6</td></tr><tr><td>PoseDiffusion [34]</td><td>63.2</td><td>64.2</td><td>64.2</td><td>65.7</td><td>66.2</td><td>67.0</td><td>67.7</td><td>100</td><td>63.6</td><td>50.5</td><td>45.7</td><td>43.0</td><td>41.2</td></tr><tr><td>RelPose++ [12]</td><td>69.8</td><td>71.1</td><td>71.9</td><td>72.8</td><td>73.8</td><td>74.4</td><td>74.9</td><td>100</td><td>70.6</td><td>58.8</td><td>53.4</td><td>50.4</td><td>47.8</td></tr><tr><td>RayDiffusion [41]</td><td>83.5</td><td>85.6</td><td>86.3</td><td>86.9</td><td>87.2</td><td>87.5</td><td>88.1</td><td>100</td><td>87.7</td><td>81.1</td><td>77.0</td><td>74.1</td><td>72.4</td></tr><tr><td>DUSt3R-CO3D [36]</td><td>79.8</td><td>81.5</td><td>82.6</td><td>82.7</td><td>83.0</td><td>83.3</td><td>83.7</td><td>100</td><td>83.6</td><td>77.2</td><td>71.8</td><td>70.0</td><td>68.1</td></tr><tr><td>DUSt3R [36]</td><td>90.8</td><td>92.6</td><td>93.6</td><td>93.6</td><td>93.8</td><td>93.6</td><td>93.4</td><td>100</td><td>87.9</td><td>79.8</td><td>74.3</td><td>71.7</td><td>69.4</td></tr><tr><td>DiffusionSfM-CO3D</td><td>90.4</td><td>91.2</td><td>92.7</td><td>93.0</td><td>93.1</td><td>93.3</td><td>93.5</td><td>100</td><td>91.1</td><td>87.7</td><td>85.3</td><td>83.7</td><td>82.7</td></tr><tr><td>DiffusionSfM</td><td>91.5</td><td>92.8</td><td>93.6</td><td>93.9</td><td>94.1</td><td>94.2</td><td>94.4</td><td>100</td><td>92.4</td><td>87.9</td><td>86.2</td><td>85.3</td><td>84.1</td></tr></table>
+
+era centers (see the backpack example). Additional qualitative results on camera accuracy are provided in Fig.4.
+
+Predicted Geometry. To evaluate predicted geometry, we compute Chamfer Distance (CD) and show comparisons against baselines in Tab. 2. We compute CD in two setups (with and without foreground object mask), and find that DiffusionSfM-CO3D performs best without foreground masking. In this setup, the predicted ray endpoints corresponding to the background image pixels tend to have larger coordinate values than foreground ones, and therefore dominate CD. This result indicates that our model provides more accurate predictions for complex image backgrounds. In terms of CD with masking, DUSt3R achieves the best result, while our two model variants outperform DUSt3R-CO3D. See Fig. 3 for visualization. We also notice that naively combining RayDiffusion poses with estimated depths from MoGe does not work well, as the inferred depths are potentially inconsistent across different views, thus resulting in degraded performance.
+
+# 4.3. Evaluation on Scene-Level Datasets
+
+Beyond the object-centric CO3D dataset [21], we compare DiffusionSfM against DUSt3R on two scene-level datasets: Habitat (in-distribution) [24] and RealEstate10k (out-of-distribution) [42]. The results are presented in Tab. 3. While DiffusionSfM achieves comparable camera rotation accuracy to DUSt3R, it consistently predicts more accurate camera centers, aligning with our findings on CO3D.
+
+Table 1. Camera Rotation and Center Accuracy on CO3D. On the left, we report the proportion of relative camera rotations within  $15^{\circ}$  of the ground truth. On the right, we report the proportion of camera centers within  $10\%$  of the scene scale, relative to the ground truth. To align the predicted camera centers to ground truth, we apply an optimal similarity transform  $(s, \mathbf{R}, \mathbf{t})$ , hence the alignment is perfect at  $N = 2$  but worsens with more images. DiffusionSfM outperforms all other methods for camera center accuracy, and outperforms all methods trained on equivalent data for rotation accuracy.  
+
+<table><tr><td># of Images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>RD*+MoGe [41]</td><td>0.059</td><td>0.064</td><td>0.071</td><td>0.062</td><td>0.063</td><td>0.061</td><td>0.061</td></tr><tr><td>DUSt3R* [36]</td><td>0.036</td><td>0.037</td><td>0.040</td><td>0.040</td><td>0.037</td><td>0.036</td><td>0.039</td></tr><tr><td>DUSt3R [36]</td><td>0.021</td><td>0.023</td><td>0.024</td><td>0.024</td><td>0.025</td><td>0.025</td><td>0.023</td></tr><tr><td>DiffusionSfM*</td><td>0.019</td><td>0.021</td><td>0.022</td><td>0.022</td><td>0.021</td><td>0.021</td><td>0.021</td></tr><tr><td>DiffusionSfM</td><td>0.025</td><td>0.025</td><td>0.025</td><td>0.025</td><td>0.026</td><td>0.025</td><td>0.028</td></tr><tr><td>RD*+MoGe [41]</td><td>0.071</td><td>0.075</td><td>0.068</td><td>0.067</td><td>0.066</td><td>0.064</td><td>0.064</td></tr><tr><td>DUSt3R* [36]</td><td>0.038</td><td>0.036</td><td>0.036</td><td>0.036</td><td>0.034</td><td>0.033</td><td>0.034</td></tr><tr><td>DUSt3R [36]</td><td>0.023</td><td>0.022</td><td>0.019</td><td>0.020</td><td>0.019</td><td>0.020</td><td>0.020</td></tr><tr><td>DiffusionSfM*</td><td>0.028</td><td>0.025</td><td>0.024</td><td>0.024</td><td>0.024</td><td>0.023</td><td>0.022</td></tr><tr><td>DiffusionSfM</td><td>0.027</td><td>0.024</td><td>0.023</td><td>0.022</td><td>0.022</td><td>0.022</td><td>0.021</td></tr></table>
+
+Table 2. Chamfer Distance  $(\downarrow)$  on CO3D Unseen Categories. Top: CD computed on all scene points. Bottom: CD computed on foreground points only. Models marked with “*” are trained on CO3D only, while those without are trained on multiple datasets. Note that top and bottom values are not directly comparable, as each ground-truth point cloud is individually normalized.
+
+# 4.4. Inference Speed
+
+Though our method requires iterative diffusion denoising at inference, we can speed this up by performing early stopping. Specifically, we can treat the  $x_0$ -prediction from early timesteps as our output instead of iterating over all denoising timesteps. Consistent with observations by Zhang et al. [41], this in fact yields more accurate predictions than the final-step diffusion outputs. As a result we only require 10 denoising diffusion timesteps for inference, taking 1.91
+
+<table><tr><td rowspan="2">Hab.</td><td>DUSt3R</td><td>97.0/100</td><td>95.0/97.6</td><td>94.3/95.0</td><td>94.2/93.1</td></tr><tr><td>DiffusionSfM</td><td>92.6/100</td><td>93.7/99.1</td><td>94.2/98.8</td><td>94.9/98.6</td></tr><tr><td rowspan="2">RE10</td><td>DUSt3R</td><td>98.1/100</td><td>97.7/68.7</td><td>97.6/57.9</td><td>97.7/53.3</td></tr><tr><td>DiffusionSfM</td><td>97.8/100</td><td>97.5/75.6</td><td>97.7/66.2</td><td>97.9/61.9</td></tr></table>
+
+Table 3. Camera Rotation and Center Accuracy on Two Scene-Level Datasets. Top: Habitat (2-5 views). Bottom: RealEstate10k (2, 4, 6, 8 views). Each grid reports camera rotation accuracy (left,  $\uparrow$ ) and center accuracy (right,  $\uparrow$ ). While DiffusionSfM performs on par with DUSt3R in rotation accuracy, it consistently surpasses DUSt3R in center accuracy.  
+
+<table><tr><td># of Images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>DiffusionSfM*</td><td>0.019</td><td>0.021</td><td>0.022</td><td>0.022</td><td>0.021</td><td>0.021</td><td>0.021</td></tr><tr><td>w/o Mask</td><td>0.020</td><td>0.022</td><td>0.023</td><td>0.023</td><td>0.022</td><td>0.022</td><td>0.024</td></tr></table>
+
+Table 4. Ablation Study on GT Mask Conditioning for CO3D Unseen Categories. We assess the effect of replacing GT mask conditioning with depth interpolation in our CO3D variant (DiffusionSfM*), by reporting the CD for predicted geometry. Incorporating mask conditioning to indicate missing data during training improves geometry quality.
+
+seconds on a single A5000 GPU with 8 input images. In contrast, DUSt3R takes 8.73 seconds to run the complete pairwise inference and global alignment procedure. We provide additional analysis in the supplementary material.
+
+# 4.5. Ablation Study
+
+Homogeneous Coordinates. The use of homogeneous coordinates for ray origins and endpoints is crucial for stable model training. To assess its impact, we replace the proposed homogeneous representation with standard 3D coordinates in  $\mathbb{R}^3$ . Our experiments show that this variant is difficult to train and fails to converge. Further details on this experiment are provided in the supplementary material.
+
+GT Mask Conditioning. To evaluate the effectiveness of the proposed GT mask conditioning, we train a baseline model without using this strategy. For missing values in the ground-truth depth maps, we use nearest-neighbor interpolation to fill in invalid pixels. This experiment is conducted on the CO3D dataset, with results presented in Tab. 4. The findings show that removing GT mask conditioning consistently degrades predicted geometry across varying numbers of input views, even when the loss is still masked. While interpolation can effectively fill missing depth within object regions, it often introduces substantial noise in the background (e.g., the sky). This noise negatively impacts diffusion model training, as the entire ray origin and endpoint maps are used as input. We anticipate an even larger performance gap on non-object-centric datasets with more outdoor scenes, such as MegaDepth [11].
+
+![](images/73e85658c1c87772133020c3736a2822b53d306c91f74b826fc325128df9097e.jpg)  
+Figure 5. Multi-modality of DiffusionSfM. We show two distinct samples from DiffusionSfM, starting from the same input images but with different random noise. Sample 1 explains the input images by putting all flowers on the left side, while Sample 2 places one flower on each side (note the difference in the green camera's viewpoint). DiffusionSfM is able to predict multi-modal geometry distributions when the scene layout is ambiguous in the inputs.
+
+# 4.6. Multi-modality from Multiple Sampling
+
+Diffusion models enable the generation of diverse samples from challenging input images. For instance, in Fig. 5, the vase exhibits symmetric patterns, and we present two distinct predicted endpoints from DiffusionSfM, each offering a different interpretation of the flowers in the image. Compared to regression models such as DUSt3R [8], DiffusionSfM is better suited for handling uncertainty – an inherent aspect of our task – where a sparse set of input images can correspond to multiple plausible 3D scene geometry.
+
+# 5. Discussion
+
+We present DiffusionSfM and demonstrate that it recovers accurate predictions of both cameras and geometry from multi-view inputs. Although our results are promising, several challenges and open questions remain.
+
+Notably, DiffusionSfM employs a pixel-space diffusion model, in contrast to the latent-space models adopted by state-of-the-art T2I generative systems. Operating in pixel space may require greater model capacity, yet our current model remains relatively small - potentially explaining the noisy patterns observed along object boundaries. Learning an expressive latent space for ray origins and endpoints by training a VAE could be a promising direction for future work. In addition, the compute requirement in multi-view transformers scales quadratically with the number of input images: one would require masked attention to deploy systems like ours for a large set of input images.
+
+Despite these challenges, we believe that our work highlights the potential of a unified approach for multi-view geometry tasks. We envision that our approach can be built upon to train a common system across related geometric tasks, such as SfM (input images with unknown origins and endpoints), registration (some images have known origins and endpoints, whereas others don't), mapping (known rays but unknown endpoints), and view synthesis (unknown pixel values for known rays).
+
+Acknowledgements: We thank the members of the Physical Perception Lab at CMU for their valuable discussions, and extend special thanks to Yanbo Xu for his insights on diffusion models.
+
+This work used Bridges-2 [4] at Pittsburgh Supercomputing Center through allocation CIS240166 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296. This work was supported by Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government.
+
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+        "type": "text",
+        "text": "Digital Twin Catalog: A Large-Scale Photorealistic 3D Object Digital Twin Dataset",
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+        "text": "Zhao Dong $^{1}$  Ka Chen $^{1,*}$  Zhaoyang Lv $^{1,*}$  Hong-Xing Yu $^{2,*}$  Yunzhi Zhang $^{2,*}$  Cheng Zhang $^{1,*}$  Yufeng Zhu $^{1,*}$  Stephen Tian $^{2}$  Zhengqin Li $^{1}$  Georgie Moffatt $^{1}$  Sean Christofferson $^{1}$  James Fort $^{1}$  Xiaqing Pan $^{1}$  Mingfei Yan $^{1}$  Jiajun Wu $^{2}$  Carl Yuheng Ren $^{1}$  Richard Newcombe $^{1}$",
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+        "text": "$^{1}$ Meta Reality Labs Research Stanford University",
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+        "image_caption": [
+            "(a) Examples of 2,000 digital twins of real-world objects"
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+            "(b) Shape & PBR Materials"
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+        "image_caption": [
+            "(c) DSLR Data",
+            "Figure 1. The Digital Twin Catalog (DTC) dataset comprises 2,000 digital twins of physical-world objects (a), characterized by millimeter-level geometric accuracy and photorealistic PBR materials (b). DTC includes evaluation data captured using both DSLR cameras and egocentric Aria glasses, featuring captured images with precise foreground object masks and environment lighting for relighting evaluation."
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+        "image_caption": [
+            "(d) Egocentric Data"
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "text": "We introduce Digital Twin Catalog (DTC), a new large-scale photorealistic 3D object digital twin dataset. A digital twin of a 3D object is a highly detailed, virtually indistinguishable representation of a physical object, accurately capturing its shape, appearance, physical properties, and other attributes. Recent advances in neural-based 3D reconstruction and inverse rendering have significantly improved the quality of 3D object reconstruction. Despite these advancements, there remains a lack of a large-scale, digital twin quality real-world dataset and benchmark that can quantitatively assess and compare the performance of different reconstruction methods, as well as improve reconstruction quality through",
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+    {
+        "type": "text",
+        "text": "training or fine-tuning. Moreover, to democratize 3D digital twin creation, it is essential to integrate creation techniques with next-generation egocentric computing platforms, such as AR glasses. Currently, there is no dataset available to evaluate 3D object reconstruction using egocentric captured images. To address these gaps, the DTC dataset features 2,000 scanned digital twin-quality 3D objects, along with image sequences captured under different lighting conditions using DSLR cameras and egocentric AR glasses. This dataset establishes the first comprehensive real-world evaluation benchmark for 3D digital twin creation tasks, offering a robust foundation for comparing and improving existing reconstruction methods. The DTC dataset is already released at https://www.projectaria.com/datasets/dtc/ and we will also make the baseline evaluations open-source.",
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+    {
+        "type": "header",
+        "text": "CVF",
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+    {
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "*Authors contributed equally and are listed in alphabetical order.",
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+        "image_caption": [
+            "Figure 2. Example DTC models with photorealistic PBR materials."
+        ],
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "A digital twin of a 3D object is a highly detailed, virtually indistinguishable representation of a physical object, capturing its shape, appearance, physical properties and other attributes with precision. Such a digital twin enables visualization, analysis, and interaction as if it were the real object, supporting simulation, automation, and real-world problem-solving across a wide range of applications in AR/VR [3, 28], spatial/contextual AI [2], and robotics [23, 43]. As fundamental properties of an object, its shape and appearance form the basis for recognizing and interpreting the 3D object, enabling identification, manipulation, and realistic rendering. Recovering these attributes has long been a foundational topic in computer vision and graphics, inspiring extensive research in 3D reconstruction and inverse rendering. Recent breakthroughs in neural-based representation and reconstruction techniques, such as NeRF [52] and 3D Gaussian splattig (3DGS) [37], have significantly elevated the quality of novel view synthesis (NVS) to photorealistic levels. Many subsequent works [35, 62] integrate neural reconstruction with physically-based inverse rendering, enabling relightable appearances. Furthermore, leveraging priors from large reconstruction models (LRMs) [30], high-quality shape and appearance reconstruction can now be achieved with as few as one to four views [41, 69, 82].",
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+    {
+        "type": "text",
+        "text": "Despite the rapid advancements in 3D object reconstruction, one question remains: does the reconstruction quality truly meet the standard of a digital twin, where virtual representations are indistinguishable from reality? This digital twin standard demands both highly accurate shape matching and photorealistic appearance across different lighting, which present significant acquisition challenges for real-world objects. Existing object-centric datasets for 3D recon",
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+    {
+        "type": "text",
+        "text": "struction or inverse rendering have focused on either dataset size [18] or quality of specific aspects [16, 21, 34, 46, 61, 73], often sacrificing comprehensive fidelity and limiting their application scope. This trade-off has led to a lack of datasets that fully satisfy the digital twin criteria, hindering current 3D reconstruction methods from achieving digital twin fidelity. To bridge this gap, we developed the Digital Twin Catalog (DTC) dataset, comprising 2,000 scanned 3D object models (Fig. 1(a)), each with millimeter geometry accuracy and photorealistic PBR materials (Fig. 1(b), Fig. 2).",
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+    {
+        "type": "text",
+        "text": "In addition to 3D digital twin models, the DTC dataset includes evaluation data designed to support 3D object reconstruction research. This evaluation data features multiview image sequences with precise foreground object masks and environment lighting information for relighting evaluation. Traditionally, high-quality HDR images captured with modern DSLR cameras have been the standard for 3D reconstruction research. Looking ahead, we encourage the integration of 3D reconstruction research with next-generation human-centric computing platforms, such as egocentric AR glasses, aiming to democratize 3D reconstruction techniques and empower everyone to effortlessly create 3D digital twins. To this end, alongside DSLR-captured evaluation data (Fig. 1(c)), the DTC dataset also provides egocentric evaluation data captured using Project Aria glasses (https://www.projectaria.com) (Fig. 1(d)).",
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+    {
+        "type": "text",
+        "text": "The DTC dataset offers extensive opportunities for advancing research in object digital twin creation. We provide a benchmark for state-of-the-art 3D object reconstruction and inverse rendering methods. These benchmarks evaluate performance across novel view synthesis (NVS), shape reconstruction, and relightable appearance reconstruction. We further provide the evaluation of novel view synthesis meth",
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+        "text": "754",
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+    {
+        "type": "table",
+        "img_path": "images/bb306c32194b753c9ba465301f050069d8d24047d747150c927252e682122167.jpg",
+        "table_caption": [
+            "Table 1. Comparison with existing object-centric inverse rendering datasets. *Objaverse [18] consists of both synthetic objects and real scans, only part of which contain PBR materials."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td># Objects</td><td>Real</td><td>Scene Type</td><td>Multi-view</td><td>Shape</td><td>PBR Mat.</td><td>Relit Image</td><td>Lighting</td><td>Egocentric Cap.</td></tr><tr><td>ShapeNet-Intrinsics [61]</td><td>31K</td><td>X</td><td>synthetic</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>NeRD Synthetic [11]</td><td>3</td><td>X</td><td>synthetic</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>ABO [16]</td><td>8K</td><td>X</td><td>synthetic</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>MIT Intrasins [25]</td><td>20</td><td>✓</td><td>studio</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DTU-MVS [34]</td><td>80</td><td>✓</td><td>studio</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Objaverse [18]</td><td>818K</td><td>(✓)*</td><td>studio</td><td>✓</td><td>✓</td><td>(✓)*</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DiLiGenT-MV [42]</td><td>5</td><td>✓</td><td>studio</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>ReNe [65]</td><td>20</td><td>✓</td><td>studio</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>OpenIllumination [46]</td><td>64</td><td>✓</td><td>studio</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>GSO [21]</td><td>1030</td><td>✓</td><td>studio</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Lombardi et al. [47]</td><td>6</td><td>✓</td><td>in-the-wild</td><td>X</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>NeRD Real [11]</td><td>4</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>NeROIC [38]</td><td>3</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Oxholm et al. [56]</td><td>4</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>OmniObject3D [73]</td><td>6k</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Stanford Orb [39]</td><td>14</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>DTC (ours)</td><td>2k</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "ods using the egocentric aligned DTC data. Additionally, we explore the dataset's potential in downstream robotics applications by assessing its effectiveness in training robotic policies for pushing and grasping tasks in simulation. These benchmarks and applications provide valuable insights, highlight existing challenges, and uncover promising directions for future research in 3D digital twin creation.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
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+        "text": "We provide a comparison of our DTC dataset to existing object-centric datasets in Table 1. We provide the largest 3D dataset with PBR materials and real world multi-view recordings with digital twin counterparts. We further provide digital twin aligned egocentric recordings, the first of their kind in the egocentric domain. We will discuss the related datasets and methods they can empower as follows.",
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+        "text": "3D Digital Twin Datasets Existing 3D digital twin datasets with PBR materials often serve as ground truth for evaluating inverse rendering results. Early efforts [6, 25] provide small-scale intrinsic image of real objects and do not provide shape or PBR material information. Synthetic datasets [11, 16, 45, 61, 70, 72] are widely used for evaluation but do not represent the complexity in a real world environment. For datasets that contain real objects, [18, 34, 42, 47, 56, 65], the reconstruction quality can vary, which leads to imprecise evaluations. Table 1 provides a comparison to the previous work in this domain. Compared to Objaverse[18, 19], which is a collection of existing 3D models with only a small subset containing PBR materials with varying quality, we offer a high quality collection of 3D object data that is also aligned with real world recordings. Compared to OmniObject3D [73], the DTC models",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "provide higher-quality shape and additional PBR materials that are necessary for high quality inverse rendering. We offer the largest quantity of 3D object models compared to all counterparts in various tasks. For real-world evaluation, Stanford-ORB [39] was the prior largest inverse rendering benchmark with in-the-wild lighting. In contrast, we provide more object diversity and higher quality for each object model. The Aria Digital Twin dataset [58] was the first dataset to provide digital twin aligned environments for the scenes and recorded using egocentric device. However, their scene environments are limited and the contained object ground truths inside do not have high quality geometries with PBR materials.",
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+    {
+        "type": "text",
+        "text": "Object Reconstruction & Inverse Rendering. Using object-centric multi-view images as input, early object reconstruction methods focused on estimating individual object properties, such as shape from shading [5, 9, 83], material acquisition [44, 45, 56, 57, 74], and lighting estimation [67, 78]. Some approaches also aimed to recover reflectance and illumination assuming known object shapes [47, 48]. Inverse rendering, which seeks to invert the rendering equation [36], estimates an image's intrinsic components—geometry, materials, and lighting. The advent of differentiable renderers [14, 15, 49] enabled full-fledged inverse rendering methods to simultaneously recover all these properties for object reconstruction [50].",
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+    {
+        "type": "text",
+        "text": "Neural volumetric representations such as Neural Radiance Fields (NeRFs) [52] and the like [7, 11-13, 59, 79, 84] encode geometry and appearance as volumetric densities and radiance with a Multi-Layer Perceptron (MLP) network, and render images using the volume rendering equation [51]. 3D-GS [37] introduces 3D Gaussian primitives and rasterization and its following-up variants [31] demonstrates high quality",
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+    {
+        "type": "page_number",
+        "text": "755",
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+    {
+        "type": "text",
+        "text": "geometry prediction as well.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Other surface-based representations [29, 53, 62, 66, 71, 80, 81, 85] extract surfaces as the zero level set, for instance, of a signed distance function (SDF) or an occupancy field [55], allowing them to efficiently model the appearance on the surface with an explicit material model, such as bidirectional reflectance distribution functions (BRDFs). This also enables modeling more complex global illumination effects, such as self-shadows. Most of these methods focus on per-scene optimization and require dense multiple views as input. Recently, researchers have incorporated learning-based models, distilling priors from large training datasets for fast inference on limited test views [8, 10, 33, 45, 61, 70, 72, 86].",
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+    {
+        "type": "text",
+        "text": "In this work, we provide the DTC dataset with real-world object recordings that can serve as the benchmark to evaluate object-centric inverse rendering tasks. We evaluate representative baselines from existing work.",
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+    {
+        "type": "text",
+        "text": "3. Digital Twin Catalog: A Large-Scale Photorealistic 3D Object Digital Twin Dataset",
+        "text_level": 1,
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+        "type": "text",
+        "text": "3.1. Dataset Composition",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our DTC dataset contains: (1) 2,000 scanned 3D object models, featuring millimeter geometric accuracy relative to their physical counterparts, along with a full set of photorealistic PBR material maps (Fig. 1), (2) 100 DSLR-captured evaluation data of 50 objects under different lighting conditions, and (3) 200 egocentric Aria-captured evaluation data of 100 objects with both active and casual observation modes.",
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+    {
+        "type": "text",
+        "text": "3.2. Creation of 3D Object Models",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Utilizing the state-of-the-art industrial 3D object scanner [1], we selected 2,000 physical-world objects spanning 40 LVIS [27] categories, carefully chosen to ensure both category diversity and compatibility with the scanner's capabilities. As illustrated in Fig. 3(a) (c), the scanner features a fixed lighting-camera setup within an upper-hemisphere dome, equipped with 8 structured lights for geometry scanning, and 29 spotlights and 29 cameras for material acquisition. During the scanning process, the object is placed on a central holder, and its pose can be adjusted with multi-round scanning to achieve a complete 360-degree scan. For our dataset, each object typically undergoes three pose changes, with a total scanning time of approximately 20 minutes per object.",
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+    {
+        "type": "text",
+        "text": "After scanning, a proprietary post-processing pipeline reconstructs both the geometry and the PBR material maps. For 4K-resolution PBR material maps, the post-processing requires approximately 4 hours per object. In terms of quality, the structured-light-based shape reconstruction (Fig. 3 (b)) in the post-processing achieves millimeter-level geometric accuracy. However, the material optimization process",
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+        "img_path": "images/1e2df084aba61005a1fff73ede9c775b1492db5fa33bf103bb57e655c46b4ffc.jpg",
+        "image_caption": [
+            "Figure 3. 3D object scanner by Covision Media®."
+        ],
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+        "bbox": [
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+        "img_path": "images/c7579deec3fdec506ecd75bef2a02066e26fe418be49935994c28f186ed5f5bc.jpg",
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+    {
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+        "img_path": "images/ea01e0790fab617bd0e4f3f993dbf25516efb0989fd13c4c1b2cf25eb8b087e6.jpg",
+        "image_caption": [
+            "Figure 4. Rendered DTC models (left) v.s. Photo (Right)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "performs best for diffuse objects and often struggles with glossy or shiny surfaces. To address this limitation, we hired technical artists to develop a workflow to refine materials for glossy and shiny objects, ensuring that the material quality meets the standards of a digital twin.",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "756",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/788b6a091b4172786c2a711155a41ca86b1db107b1def661f06eda6b8ac10fa2.jpg",
+        "image_caption": [
+            "Figure 5. Shape and material (albedo) quality comparison between Stanford-ORB [39] (left) and our DTC (right)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3D Model Accuracy. To validate the material and geometry accuracy of the 3D models, we compared a rendered image of our scanned and processed model with a photograph of the same object taken inside a light box. A virtual light box was meticulously modeled to replicate the light intensity and color temperature of the real light box. The scanned object was then placed in the virtual light box to generate the rendered image. The side-by-side comparison demonstrates a remarkable match between the rendered and real images (Fig. 4).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison Against Stanford-ORB. We also scanned the objects used in Stanford-ORB [39] to compare the shape and appearance quality. As illustrated in Fig. 5, the Stanford-ORB models exhibit shape artifacts and noisy, lower-quality materials compared to our models.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. DSLR Evaluation Data",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Within DTC, we include a DSLR-captured evaluation dataset of 50 objects from Sec. 3.2 captured under two different lighting conditions, resulting in 100 distinct image sequences. For every sequence, we provide (a) approximately 120 HDR and LDR images from different viewing directions, (b) one object pose and (c) per-image camera pose. The two lighting conditions are represented using two environment maps.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Data Capture. To ensure the DSLR evaluation data quality, we designed and built a DSLR camera rig to automate the capture process (Fig. 6). The rig is designed to rotate the cameras around the centralized object, assuming the environment lighting remains unchanged during the capture. It features a motorized rotary stage with a centrally mounted stationary platform. Attached to the rotary stage is an extrusion frame that forms the gantry arm, supported by a set of castors to bear its weight and enable smooth rotation around the central axis. The extrusion frame is equipped with adjustable camera mounts, allowing DSLR cameras to be positioned flexibly to optimize the capture setup. For our capture process, we utilized three DSLR cameras to perform a 360-degree rotation around the object, capturing images at 9-degree intervals, resulting in 120 photos per object. To ensure precise camera pose estimation, a ChArUco board",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1a6ce4a894ebbfcfb6ec2630ff256afe74443ffa2f522328986bb4e235917f94.jpg",
+        "image_caption": [
+            "Figure 6. DSLR rig for capturing evaluation data."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "was placed beneath the object during the capture. Example images from this setup are shown in Fig. 6.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Environment Maps. Following a similar approach in Stanford-ORB [39], we capture the two environment maps using chrome ball images obtained with the capture rig described earlier. With precise camera poses provided by a ChArUco board placed beneath the chrome ball, we first fit a synthetic 3D sphere to the chrome ball by optimizing its 3D position using a geometry-friendly differentiable renderer [40, 75]. Subsequently, using a differentiable Monte Carlo-based renderer [32], we refine the environment map to match the reflection on the chrome ball, employing the single-view light estimation method proposed in [78]. The coordinate system of the environment map is determined by the ChArUco detection.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Pose Registration for Camera and Object. We first obtain the initial camera poses using the ChArUco board. In most cases, for images captured from the top and middle views, the pose estimates are typically accurate. However, for bottom-view images, inaccuracies arise due to pattern distortion at grazing angles. To mitigate this issue, we refine the camera poses by fitting the rendering of a virtual ChArUco board to the real captured photo using a differentiable renderer [32, 40, 75]. Once the camera poses have been accurately refined, we optimize the object pose by minimizing the mask loss between the rendered mask and the reference one generated by [62]. By providing separate poses for camera and object anchored by ChArUco, the cameras and object are automatically aligned with the optimized environment maps.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.4. Egocentric Evaluation Data",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We include an evaluation dataset of real world recordings captured by an egocentric device paired with 100 objects from the DTC dataset. We capture the egocentric recordings using the open-sourced Project Aria device [22] and acquire the additional 3D ground truth using its machine perception tool, which includes online device calibration, device trajectory and semi-dense point clouds for each recording. Each recording contains a single 3D object and precisely aligned object poses in the Aria trajectory coordinate frame.",
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+        "page_idx": 4
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+    {
+        "type": "page_number",
+        "text": "757",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/dcd62f9fc15c847d5a6c0ee8cc41a039480a020f8dc5ae093f19a24eaae0f820.jpg",
+        "image_caption": [
+            "Figure 7. The workflow to align egocentric video and 3D objects. We acquire the object's semi-dense point cloud from the egocentric recording and the neural reconstructed mesh using Neural-PBIR [62]. Finally, we align the 3D object with the rendered mask from the neural reconstructed mesh using physics-based differentiable rendering (PBDR)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Both the object and the trajectory are in metric scale. We can derive additional ground truth for each video from the aligned 3D object properties.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Data Capture. To feature real world recordings observed from human perspectives that can be representative of 3D object reconstruction for AR/MR devices or robots, we provide two types of recording trajectories for selected objects, termed active and passive respectively, collected by human wearers. The active recording features a complete 360 view of the objects, which is similar to existing object 3D novel view synthesis dataset. The passive recording features casual looks from human wearer, which only contain partial views of the object from certain viewing angles along the trajectory. In dataset creation, we collected the active and passive recordings in the same environment and generate their 3D information in the shared 3D space. This helps reduces potential failures when aligning the object to passive 3D recordings, which are shorter and contains less 3D information. To reduce the effect of noises and motion blur, which are common in egocentric videos in indoor low light environments, we light the capture environment to  $3\\mathrm{K}+$  lux illumination and used a fixed low-exposure and gain profile to collect each recording with the appropriate brightness.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Alignment between Egocentric Video and Object. We provide an illustration of the object alignment to the egocentric video in Fig. 7. Given the images, camera poses and semi-dense point cloud acquired from Project Aria tools, we employ a neural-based mesh reconstruction method [62] to",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "create reference meshes for generating high-quality reference masks and used that to align with the corresponding 3D object mesh. This alignment step serves as an initialization for a more precise pose refinement, which leverages differentiable rendering. For certain objects with symmetric geometry, we observe this process can introduce ambiguities in point cloud registration and subsequent failures. To address such cases, we provide a GUI to manually align and correct the object alignment. Finally, akin to the DSLR camera pose registration phase, we optimize a mask loss over object poses to achieve fine-tuned pose registration.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4. Benchmarking and Applications",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We first use our DLSR and egocentric dataset as a benchmark for existing state-of-the-art methods. For inverse rendering, we design metrics to evaluate the shape and material quality of the recovered 3D object digital twin from three perspectives. For egocentric recording, we evaluate the novel-view synthesis as the initial evaluation. We include additional tasks, e.g. sparse view reconstruction in the supplementary materials for both DSLR and egocentric recordings. Finally we can demonstrate our high quality 3D digital twin models can be beneficial to robotics domain using an application in robotics manipulation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.1. Application to Inverse Rendering for DSLR",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The DSLR dataset in DTC provides accurate ground truth, including poses, lighting and 3D models, for inverse rendering",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "758",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/66a1b9d8428860a6cacaef98e9368932c4ff416345451293221c6ba11ddb4a8d.jpg",
+        "table_caption": [
+            "Table 2. Benchmark comparison of existing methods on inverse rendering for DSLR. Depth SI-MSE and Shape Chamfer distance  $\\times  {10}^{-3}$  ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"3\">Geometry</td><td colspan=\"4\">Novel Scene Relighting</td><td colspan=\"4\">Novel View Synthesis</td></tr><tr><td>Depth↓</td><td>Normal↓</td><td>Shape↓</td><td>PSNR-H↑</td><td>PSNR-L↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR-H↑</td><td>PSNR-L↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>Neural-PIL [12]</td><td>5.71</td><td>0.25</td><td>25.02</td><td colspan=\"4\">N/A</td><td>28.42</td><td>35.76</td><td>0.882</td><td>0.096</td></tr><tr><td>PhySG [80]</td><td>0.31</td><td>0.16</td><td>11.31</td><td>27.28</td><td>32.86</td><td>0.959</td><td>0.049</td><td>28.54</td><td>34.46</td><td>0.964</td><td>0.045</td></tr><tr><td>NVDiffRec [53]</td><td>0.02</td><td>0.07</td><td>1.64</td><td>26.99</td><td>33.27</td><td>0.951</td><td>0.037</td><td>28.95</td><td>34.92</td><td>0.967</td><td>0.029</td></tr><tr><td>NeRD [11]</td><td>4.55</td><td>0.45</td><td>108.20</td><td>26.10</td><td>32.60</td><td>0.948</td><td>0.061</td><td>26.80</td><td>33.40</td><td>0.882</td><td>0.102</td></tr><tr><td>InvRender [71]</td><td>0.22</td><td>0.03</td><td>0.75</td><td>29.52</td><td>35.98</td><td>0.961</td><td>0.037</td><td>31.64</td><td>37.82</td><td>0.970</td><td>0.033</td></tr><tr><td>NVDiffRecMC [29]</td><td>0.02</td><td>0.06</td><td>1.34</td><td>27.78</td><td>34.55</td><td>0.952</td><td>0.042</td><td>31.27</td><td>38.17</td><td>0.972</td><td>0.032</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a234b44032efe9c9f6c7f33fd20e7e0ecc49d74e3d089a7a4236cf3cccd9627d.jpg",
+        "table_caption": [
+            "Table 3. Benchmark on the egocentric aligned recordings."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>PSNR ↑</td><td>LPIPS ↓</td><td>SSIM ↑</td><td>Depth ↓</td><td>Normal ↓</td></tr><tr><td>3D-GS [37]</td><td>28.81</td><td>0.020</td><td>0.9888</td><td>0.1768</td><td>0.3301</td></tr><tr><td>2D-GS [31]</td><td>28.75</td><td>0.020</td><td>0.9886</td><td>0.1755</td><td>0.2112</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "tasks and serves as an evaluation suite to benchmark the performance of inverse rendering methods. We select six prior methods for this task and evaluate their performance using the ground truth provided by our dataset. In the following sections, we describe the data splitting strategy, evaluation metrics, and baselines.",
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+    },
+    {
+        "type": "text",
+        "text": "Data Splitting. For benchmarking purposes, we select 15 objects from the DSLR dataset captured under two distinct lighting environments, resulting in a total of 30 image sequences. The selected objects encompass a diverse range of geometric and material properties to ensure a comprehensive evaluation. For each scene, 8 views are selected for testing, while the remaining views are reserved for training.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. The metrics measure the accuracy of three aspects of baseline performance: geometry estimation, relighting, and novel view synthesis. For geometry estimation, we evaluate the accuracy of predicted depth and normal maps under held-out test views, as well as 3D meshes extracted from baseline methods, compared with the ground truth from our dataset. Relighting metrics evaluate the material decomposition quality of baselines by measuring the accuracy of predicted images under held-out lighting conditions. For view synthesis, we compare the predicted images from viewpoints unseen during training to ground truth captures. We refer to Kuang et al. [39] for metric details.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We include the following baselines: NVDiffRec [53] and NVDiffRecMC [29], with a hybrid shape representation DMTet [60]; InvRender [85] and PhySG [80], which adopt signed distance functions (SDFs) to represent object geometry [76] and utilize implicit neural fields for material decomposition; Neural-PIL [12] and NeRD [11], which use NeRFs [52] as scene representations.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Application to Egocentric Reconstruction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our digital twin models, aligned with real world video using the method described in Sec. 3.4, can help obtain accurate",
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+    {
+        "type": "text",
+        "text": "ground truth for object-centric images that were previously difficult to acquire. We provide the first evaluation of object-centric novel view synthesis recorded from an egocentric device. We use the projected object shape given the 3D pose of the object and cameras in scene coordinates to acquire the image masks, depth and normal for each object. We selected 15 recordings from the egocentric recording sessions as the evaluation and used the active recordings to benchmark novel view reconstruction. For each recording, we hold out every 8th image view as a testing view.",
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+        "text": "**Evaluations.** We build our baselines based on the gsplats [77] implementation of the 3D Gaussian Splitting (GS) [37] and 2D GS [31], and handle the effect of lens shading from the Project Aria lens [26]. We calculate PSNR, depth and normal based on the observed objects with masks and provide SSIM and LPIPS score on images by masking out the non-object areas as black. Table 3 shows the benchmark results of the baselines. We use the same depth and normal metric in DSLR evaluation. We provide additional qualitative evaluations and analyses on egocentric data towards sparser view settings in the supplementary materials.",
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+    {
+        "type": "text",
+        "text": "4.3. Application to Robotic Manipulation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "High-quality object models have been leveraged in prior work to train real-world robotic agents in scenes represented explicitly [54] or implicitly [64]. These object models have also been shown to facilitate object-centric pose and lighting parameter estimation, enabling model-based planning [63]. In this section, we empirically evaluate the effectiveness of using DTC dataset objects in training robotic policies. Specifically, we consider learning robotic pushing and grasping skills in simulation.",
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+        "type": "text",
+        "text": "First, we sample a subset of 24 cup category objects from the DTC dataset and 24 cup objects from Objaverse-XL [19]  ${}^{1}$  . Since not all Objverse-XL objects come with textures, we randomize the colors of those objects uniformly in RGB space. To compute collision meshes for physical simulation, we perform convex decomposition on each object with CoACD [68]. We import these objects along with a UR5e robot equipped with a Robotiq 2F-85 (pushing) or",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>The version of Objaverse-XL used in this work excludes all 3D models sourced from Sketchfab.",
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+        "type": "page_number",
+        "text": "759",
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+    {
+        "type": "table",
+        "img_path": "images/a6ab799d2042df478496745334f08ef485d78cac29c002571b9ec76578bd80f9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Task</td><td>DTC (ours)</td><td>Objverse-XL [19]</td></tr><tr><td>Pushing @ 2cm</td><td>36.3% ± 1.5%</td><td>25.3% ± 6.0%</td></tr><tr><td>Pushing @ 3cm</td><td>43.7% ± 1.2%</td><td>29.7% ± 6.0%</td></tr><tr><td>Pushing @ 5cm</td><td>47.0% ± 2.6%</td><td>40.3% ± 5.5%</td></tr><tr><td>Grasping</td><td>42.7% ± 4.7%</td><td>38.6% ± 11.0%</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4. Success rate of policies trained on data collected using objects from our DTC dataset and sampled from Objaverse-XL when evaluated on an unseen test object. Errors indicate sample standard deviation over three policy training seeds.",
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+    {
+        "type": "text",
+        "text": "Robotiq 2F-140 (grasping) gripper into the PyBullet simulator [17] and collect data for each robotic task as described below. After training policies on data from each object set, we evaluate policy performance on a relatively high-quality unseen test object from the StanfordORB dataset [39].",
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+        "type": "text",
+        "text": "Pushing. For the pushing task, we collect 5000 trajectories of pseudo-random robotic interaction data for each object set. For each trajectory, a single object from the considered object set and its initial position are randomly selected. Then we train a goal-conditioned neural network policy  $\\pi (a|o,o_g)$  where  $o$  is an image observation of the current scene and  $o_{g}$  is a goal image indicating the desired final object and robot position,  $o,o_{g}\\in \\mathbb{R}^{256\\times 256\\times 3}$ , and the action  $a\\in \\mathbb{R}^2$  represents a change in the robot's end-effector position in the  $x$  and  $y$  axes. The  $z$  axis end-effector height is held fixed. We sample goals for training via hindsight relabeling [4, 20, 24]. We then perform evaluation on 100 randomly sampled test goals manipulating an unseen test cup from StanfordORB [39].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Grasping. For grasping, we collect 5000 successful grasp examples for each object set by first placing a single object into the scene, randomizing the object identity and initial position. We then randomly sample candidate grasp poses in a radius around the object's position and simulating their outcomes, rejecting unsuccessful grasps. We train a grasping policy  $\\pi(a|o)$  where  $o \\in \\mathbb{R}^{256 \\times 256 \\times 3}$  is an image observation of the scene and  $a \\in \\mathbb{R}^4$  represents the  $x, y, z$  position and  $\\theta$  yaw rotation of the robot end-effector at which to attempt the grasp. Again we use 100 test cup object poses.",
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+    },
+    {
+        "type": "text",
+        "text": "Results. We report the results in Table 4 and Fig. 8. We find that across both pushing and grasping tasks, policies trained on DTC dataset objects outperform those trained on Objaverse-XL objects when evaluated on the unseen test object. For pushing, we report performance by defining binary success thresholds based on the final Euclidean distance of the object position to the goal position. Training on DTC objects appears to be especially helpful at enabling policies to make finer adjustments, improving pushing success rates at stricter thresholds. Additional experimental details can be found in the supplementary.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/3b4d8b3f2caaf2fc9858feb7baa824272d8d29f523c49ef5c6ccb9d47ac20594.jpg",
+        "image_caption": [
+            "Figure 8. Success rates on robotic pushing task when training with our DTC objects and sampled Objaverse-XL objects. Particularly at lower error thresholds, policies trained on DTC objects outperform those trained using Objaverse-XL objects. Shaded bars represent sample standard deviations over policy training random seeds."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We presented a new large scale photorealistic 3D digital twin dataset with the real world recordings that contain its real world counterpart. We provide extensive evaluations of baselines on our DTC dataset serving as new benchmark for inverse rendering and novel view synthesis task. We also demonstrated that high quality digital twin models can be beneficial to applications in robotics domain. We believe our efforts can empower the research community to build and leverage digital twin models for future applications.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Limitations. Achieving high quality digital twin models currently requires deliberate hardware setup and human efforts in refinement. Solving this challenge without sacrificing quality can significantly further enhance the volume of digital twin models. Our hardware is also limited to objects within a certain size and can not yet recover objects that are deformable, highly specular, or transparent.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Future work. The existing digital twin model creation in DTC dataset involves lengthy post-processing and may require subjective human refinement, hindering the automation of model generation. However, recent advancements in physics-based differentiable rendering hold promise for enabling faster and more accurate creation of digital twins, especially for material reconstruction. Furthermore, building large-scale digital twins for applications will necessitate efforts to enhance the diversity in object appearance (e.g., transparent objects) and to capture additional attributes, such as physical properties and functionalities.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For robotics applications, while deploying manipulation policies learned in simulation to the real world remains generally challenging, we hope that the high-quality digital twin data provided by DTC can serve as a stepping stone towards effective sim-to-real transfer.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "760",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments. This work is in part supported by NSF CCRI #2120095, RI #2211258, and RI #2338203. YZ is in part supported by the Stanford Interdisciplinary Graduate Fellowship.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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2025/Digital Twin Catalog_ A Large-Scale Photorealistic 3D Object Digital Twin Dataset/2d29b0d5-5c08-413f-9ad0-63d98b0c6539_origin.pdf

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2025/Digital Twin Catalog_ A Large-Scale Photorealistic 3D Object Digital Twin Dataset/full.md

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+# Digital Twin Catalog: A Large-Scale Photorealistic 3D Object Digital Twin Dataset
+
+Zhao Dong $^{1}$  Ka Chen $^{1,*}$  Zhaoyang Lv $^{1,*}$  Hong-Xing Yu $^{2,*}$  Yunzhi Zhang $^{2,*}$  Cheng Zhang $^{1,*}$  Yufeng Zhu $^{1,*}$  Stephen Tian $^{2}$  Zhengqin Li $^{1}$  Georgie Moffatt $^{1}$  Sean Christofferson $^{1}$  James Fort $^{1}$  Xiaqing Pan $^{1}$  Mingfei Yan $^{1}$  Jiajun Wu $^{2}$  Carl Yuheng Ren $^{1}$  Richard Newcombe $^{1}$
+
+$^{1}$ Meta Reality Labs Research Stanford University
+
+![](images/5c6ef2dab8e54265416509670d0062d9671cdfe6f8dc0a4a7cec32c62d6f5d97.jpg)  
+(a) Examples of 2,000 digital twins of real-world objects
+
+![](images/63ea79faa2c911314cac9024de6bb70ec75275098cc717280376a3c205019268.jpg)  
+(b) Shape & PBR Materials
+
+![](images/7d21347e865b975546c4908b004218877b7eed45912281de5bc1d261d7ec61c1.jpg)  
+(c) DSLR Data  
+Figure 1. The Digital Twin Catalog (DTC) dataset comprises 2,000 digital twins of physical-world objects (a), characterized by millimeter-level geometric accuracy and photorealistic PBR materials (b). DTC includes evaluation data captured using both DSLR cameras and egocentric Aria glasses, featuring captured images with precise foreground object masks and environment lighting for relighting evaluation.
+
+![](images/8ddbce2402e3d85449771a91d3f6fe0241663684d598440c2308bf4ff77860b6.jpg)  
+(d) Egocentric Data
+
+# Abstract
+
+We introduce Digital Twin Catalog (DTC), a new large-scale photorealistic 3D object digital twin dataset. A digital twin of a 3D object is a highly detailed, virtually indistinguishable representation of a physical object, accurately capturing its shape, appearance, physical properties, and other attributes. Recent advances in neural-based 3D reconstruction and inverse rendering have significantly improved the quality of 3D object reconstruction. Despite these advancements, there remains a lack of a large-scale, digital twin quality real-world dataset and benchmark that can quantitatively assess and compare the performance of different reconstruction methods, as well as improve reconstruction quality through
+
+training or fine-tuning. Moreover, to democratize 3D digital twin creation, it is essential to integrate creation techniques with next-generation egocentric computing platforms, such as AR glasses. Currently, there is no dataset available to evaluate 3D object reconstruction using egocentric captured images. To address these gaps, the DTC dataset features 2,000 scanned digital twin-quality 3D objects, along with image sequences captured under different lighting conditions using DSLR cameras and egocentric AR glasses. This dataset establishes the first comprehensive real-world evaluation benchmark for 3D digital twin creation tasks, offering a robust foundation for comparing and improving existing reconstruction methods. The DTC dataset is already released at https://www.projectaria.com/datasets/dtc/ and we will also make the baseline evaluations open-source.
+
+![](images/787532f76f3c7d05c010f997c86ce2161ca34f8cd6a082de3e89196c9b445026.jpg)
+
+![](images/7ac0bd5a69b106213fb119b8eb13f0f3640675ae19d597720bfa6b4fffd7aae1.jpg)
+
+![](images/03814b73dbaeeceaca5b864b789e7d1bd77546a4fce1c8fba05868b819ffbd6a.jpg)
+
+![](images/162bee86384d06d222c9ba1a0dd1d208552d44bf41cf0d1b69620172067937cf.jpg)
+
+![](images/4b26a4302ba3923f69965b63cf545b83d58552ac9cb9e125720cd32dd3681f09.jpg)
+
+![](images/c1f9ec98603ce255dfa5b73ba916b26a6b329bd7b9fb068f4a227c67879135ff.jpg)
+
+![](images/c3f63b0fd71a76659fed8016ddb3d7ca9f3f5354904b2712fcdf92e3b6356eae.jpg)  
+Figure 2. Example DTC models with photorealistic PBR materials.
+
+![](images/c742133f79593415e6754d2c6e6b65a5b75e0dc5457fb9ba9d20bff3338b32a0.jpg)
+
+![](images/6d2d671251186c923beaff28ce7b2a88d1983ab8b524b097b52ad10d187569e7.jpg)
+
+![](images/33f163d2d32987871165fce759381ea7ecfb7b5057c30b7527a1a50860194a9f.jpg)
+
+# 1. Introduction
+
+A digital twin of a 3D object is a highly detailed, virtually indistinguishable representation of a physical object, capturing its shape, appearance, physical properties and other attributes with precision. Such a digital twin enables visualization, analysis, and interaction as if it were the real object, supporting simulation, automation, and real-world problem-solving across a wide range of applications in AR/VR [3, 28], spatial/contextual AI [2], and robotics [23, 43]. As fundamental properties of an object, its shape and appearance form the basis for recognizing and interpreting the 3D object, enabling identification, manipulation, and realistic rendering. Recovering these attributes has long been a foundational topic in computer vision and graphics, inspiring extensive research in 3D reconstruction and inverse rendering. Recent breakthroughs in neural-based representation and reconstruction techniques, such as NeRF [52] and 3D Gaussian splattig (3DGS) [37], have significantly elevated the quality of novel view synthesis (NVS) to photorealistic levels. Many subsequent works [35, 62] integrate neural reconstruction with physically-based inverse rendering, enabling relightable appearances. Furthermore, leveraging priors from large reconstruction models (LRMs) [30], high-quality shape and appearance reconstruction can now be achieved with as few as one to four views [41, 69, 82].
+
+Despite the rapid advancements in 3D object reconstruction, one question remains: does the reconstruction quality truly meet the standard of a digital twin, where virtual representations are indistinguishable from reality? This digital twin standard demands both highly accurate shape matching and photorealistic appearance across different lighting, which present significant acquisition challenges for real-world objects. Existing object-centric datasets for 3D recon
+
+struction or inverse rendering have focused on either dataset size [18] or quality of specific aspects [16, 21, 34, 46, 61, 73], often sacrificing comprehensive fidelity and limiting their application scope. This trade-off has led to a lack of datasets that fully satisfy the digital twin criteria, hindering current 3D reconstruction methods from achieving digital twin fidelity. To bridge this gap, we developed the Digital Twin Catalog (DTC) dataset, comprising 2,000 scanned 3D object models (Fig. 1(a)), each with millimeter geometry accuracy and photorealistic PBR materials (Fig. 1(b), Fig. 2).
+
+In addition to 3D digital twin models, the DTC dataset includes evaluation data designed to support 3D object reconstruction research. This evaluation data features multiview image sequences with precise foreground object masks and environment lighting information for relighting evaluation. Traditionally, high-quality HDR images captured with modern DSLR cameras have been the standard for 3D reconstruction research. Looking ahead, we encourage the integration of 3D reconstruction research with next-generation human-centric computing platforms, such as egocentric AR glasses, aiming to democratize 3D reconstruction techniques and empower everyone to effortlessly create 3D digital twins. To this end, alongside DSLR-captured evaluation data (Fig. 1(c)), the DTC dataset also provides egocentric evaluation data captured using Project Aria glasses (https://www.projectaria.com) (Fig. 1(d)).
+
+The DTC dataset offers extensive opportunities for advancing research in object digital twin creation. We provide a benchmark for state-of-the-art 3D object reconstruction and inverse rendering methods. These benchmarks evaluate performance across novel view synthesis (NVS), shape reconstruction, and relightable appearance reconstruction. We further provide the evaluation of novel view synthesis meth
+
+Table 1. Comparison with existing object-centric inverse rendering datasets. *Objaverse [18] consists of both synthetic objects and real scans, only part of which contain PBR materials.  
+
+<table><tr><td>Dataset</td><td># Objects</td><td>Real</td><td>Scene Type</td><td>Multi-view</td><td>Shape</td><td>PBR Mat.</td><td>Relit Image</td><td>Lighting</td><td>Egocentric Cap.</td></tr><tr><td>ShapeNet-Intrinsics [61]</td><td>31K</td><td>X</td><td>synthetic</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>NeRD Synthetic [11]</td><td>3</td><td>X</td><td>synthetic</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>ABO [16]</td><td>8K</td><td>X</td><td>synthetic</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>MIT Intrasins [25]</td><td>20</td><td>✓</td><td>studio</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DTU-MVS [34]</td><td>80</td><td>✓</td><td>studio</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Objaverse [18]</td><td>818K</td><td>(✓)*</td><td>studio</td><td>✓</td><td>✓</td><td>(✓)*</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DiLiGenT-MV [42]</td><td>5</td><td>✓</td><td>studio</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>ReNe [65]</td><td>20</td><td>✓</td><td>studio</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>OpenIllumination [46]</td><td>64</td><td>✓</td><td>studio</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>GSO [21]</td><td>1030</td><td>✓</td><td>studio</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Lombardi et al. [47]</td><td>6</td><td>✓</td><td>in-the-wild</td><td>X</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>NeRD Real [11]</td><td>4</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>NeROIC [38]</td><td>3</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Oxholm et al. [56]</td><td>4</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>OmniObject3D [73]</td><td>6k</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Stanford Orb [39]</td><td>14</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>DTC (ours)</td><td>2k</td><td>✓</td><td>in-the-wild</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+ods using the egocentric aligned DTC data. Additionally, we explore the dataset's potential in downstream robotics applications by assessing its effectiveness in training robotic policies for pushing and grasping tasks in simulation. These benchmarks and applications provide valuable insights, highlight existing challenges, and uncover promising directions for future research in 3D digital twin creation.
+
+# 2. Related Work
+
+We provide a comparison of our DTC dataset to existing object-centric datasets in Table 1. We provide the largest 3D dataset with PBR materials and real world multi-view recordings with digital twin counterparts. We further provide digital twin aligned egocentric recordings, the first of their kind in the egocentric domain. We will discuss the related datasets and methods they can empower as follows.
+
+3D Digital Twin Datasets Existing 3D digital twin datasets with PBR materials often serve as ground truth for evaluating inverse rendering results. Early efforts [6, 25] provide small-scale intrinsic image of real objects and do not provide shape or PBR material information. Synthetic datasets [11, 16, 45, 61, 70, 72] are widely used for evaluation but do not represent the complexity in a real world environment. For datasets that contain real objects, [18, 34, 42, 47, 56, 65], the reconstruction quality can vary, which leads to imprecise evaluations. Table 1 provides a comparison to the previous work in this domain. Compared to Objaverse[18, 19], which is a collection of existing 3D models with only a small subset containing PBR materials with varying quality, we offer a high quality collection of 3D object data that is also aligned with real world recordings. Compared to OmniObject3D [73], the DTC models
+
+provide higher-quality shape and additional PBR materials that are necessary for high quality inverse rendering. We offer the largest quantity of 3D object models compared to all counterparts in various tasks. For real-world evaluation, Stanford-ORB [39] was the prior largest inverse rendering benchmark with in-the-wild lighting. In contrast, we provide more object diversity and higher quality for each object model. The Aria Digital Twin dataset [58] was the first dataset to provide digital twin aligned environments for the scenes and recorded using egocentric device. However, their scene environments are limited and the contained object ground truths inside do not have high quality geometries with PBR materials.
+
+Object Reconstruction & Inverse Rendering. Using object-centric multi-view images as input, early object reconstruction methods focused on estimating individual object properties, such as shape from shading [5, 9, 83], material acquisition [44, 45, 56, 57, 74], and lighting estimation [67, 78]. Some approaches also aimed to recover reflectance and illumination assuming known object shapes [47, 48]. Inverse rendering, which seeks to invert the rendering equation [36], estimates an image's intrinsic components—geometry, materials, and lighting. The advent of differentiable renderers [14, 15, 49] enabled full-fledged inverse rendering methods to simultaneously recover all these properties for object reconstruction [50].
+
+Neural volumetric representations such as Neural Radiance Fields (NeRFs) [52] and the like [7, 11-13, 59, 79, 84] encode geometry and appearance as volumetric densities and radiance with a Multi-Layer Perceptron (MLP) network, and render images using the volume rendering equation [51]. 3D-GS [37] introduces 3D Gaussian primitives and rasterization and its following-up variants [31] demonstrates high quality
+
+geometry prediction as well.
+
+Other surface-based representations [29, 53, 62, 66, 71, 80, 81, 85] extract surfaces as the zero level set, for instance, of a signed distance function (SDF) or an occupancy field [55], allowing them to efficiently model the appearance on the surface with an explicit material model, such as bidirectional reflectance distribution functions (BRDFs). This also enables modeling more complex global illumination effects, such as self-shadows. Most of these methods focus on per-scene optimization and require dense multiple views as input. Recently, researchers have incorporated learning-based models, distilling priors from large training datasets for fast inference on limited test views [8, 10, 33, 45, 61, 70, 72, 86].
+
+In this work, we provide the DTC dataset with real-world object recordings that can serve as the benchmark to evaluate object-centric inverse rendering tasks. We evaluate representative baselines from existing work.
+
+# 3. Digital Twin Catalog: A Large-Scale Photorealistic 3D Object Digital Twin Dataset
+
+# 3.1. Dataset Composition
+
+Our DTC dataset contains: (1) 2,000 scanned 3D object models, featuring millimeter geometric accuracy relative to their physical counterparts, along with a full set of photorealistic PBR material maps (Fig. 1), (2) 100 DSLR-captured evaluation data of 50 objects under different lighting conditions, and (3) 200 egocentric Aria-captured evaluation data of 100 objects with both active and casual observation modes.
+
+# 3.2. Creation of 3D Object Models
+
+Utilizing the state-of-the-art industrial 3D object scanner [1], we selected 2,000 physical-world objects spanning 40 LVIS [27] categories, carefully chosen to ensure both category diversity and compatibility with the scanner's capabilities. As illustrated in Fig. 3(a) (c), the scanner features a fixed lighting-camera setup within an upper-hemisphere dome, equipped with 8 structured lights for geometry scanning, and 29 spotlights and 29 cameras for material acquisition. During the scanning process, the object is placed on a central holder, and its pose can be adjusted with multi-round scanning to achieve a complete 360-degree scan. For our dataset, each object typically undergoes three pose changes, with a total scanning time of approximately 20 minutes per object.
+
+After scanning, a proprietary post-processing pipeline reconstructs both the geometry and the PBR material maps. For 4K-resolution PBR material maps, the post-processing requires approximately 4 hours per object. In terms of quality, the structured-light-based shape reconstruction (Fig. 3 (b)) in the post-processing achieves millimeter-level geometric accuracy. However, the material optimization process
+
+![](images/514e435cb5ecf8ec602ac85b2b43b8a3f2c3a2d8ef0c882b2ac2ddd7d287b30e.jpg)
+
+![](images/135bc7d0496f2c9a75be1831c6bd023e92a6f80918f7d1b09193a3d349de2602.jpg)
+
+![](images/1e2df084aba61005a1fff73ede9c775b1492db5fa33bf103bb57e655c46b4ffc.jpg)  
+Figure 3. 3D object scanner by Covision Media®.
+
+![](images/2221885c36272e45c04b1bb11f68fe0926c7cc4abddbd05d5b0cb6a6dc0834fc.jpg)
+
+![](images/b6c70bcdf78249b5ac44914e03c7c6a9ce38c56777016c4c60a6be8291f00057.jpg)
+
+![](images/81e1f60c73757d07d21564f4f92073b2c070847f5d4120db339f1d4b88771dbc.jpg)
+
+![](images/c7579deec3fdec506ecd75bef2a02066e26fe418be49935994c28f186ed5f5bc.jpg)
+
+![](images/ea01e0790fab617bd0e4f3f993dbf25516efb0989fd13c4c1b2cf25eb8b087e6.jpg)  
+Figure 4. Rendered DTC models (left) v.s. Photo (Right).
+
+![](images/2dde835d30df0f67fe2c497f736b8b0b1a2f89ba0109ae86e7edd6a6d6160cc2.jpg)
+
+performs best for diffuse objects and often struggles with glossy or shiny surfaces. To address this limitation, we hired technical artists to develop a workflow to refine materials for glossy and shiny objects, ensuring that the material quality meets the standards of a digital twin.
+
+![](images/788b6a091b4172786c2a711155a41ca86b1db107b1def661f06eda6b8ac10fa2.jpg)  
+Figure 5. Shape and material (albedo) quality comparison between Stanford-ORB [39] (left) and our DTC (right).
+
+3D Model Accuracy. To validate the material and geometry accuracy of the 3D models, we compared a rendered image of our scanned and processed model with a photograph of the same object taken inside a light box. A virtual light box was meticulously modeled to replicate the light intensity and color temperature of the real light box. The scanned object was then placed in the virtual light box to generate the rendered image. The side-by-side comparison demonstrates a remarkable match between the rendered and real images (Fig. 4).
+
+Comparison Against Stanford-ORB. We also scanned the objects used in Stanford-ORB [39] to compare the shape and appearance quality. As illustrated in Fig. 5, the Stanford-ORB models exhibit shape artifacts and noisy, lower-quality materials compared to our models.
+
+# 3.3. DSLR Evaluation Data
+
+Within DTC, we include a DSLR-captured evaluation dataset of 50 objects from Sec. 3.2 captured under two different lighting conditions, resulting in 100 distinct image sequences. For every sequence, we provide (a) approximately 120 HDR and LDR images from different viewing directions, (b) one object pose and (c) per-image camera pose. The two lighting conditions are represented using two environment maps.
+
+Data Capture. To ensure the DSLR evaluation data quality, we designed and built a DSLR camera rig to automate the capture process (Fig. 6). The rig is designed to rotate the cameras around the centralized object, assuming the environment lighting remains unchanged during the capture. It features a motorized rotary stage with a centrally mounted stationary platform. Attached to the rotary stage is an extrusion frame that forms the gantry arm, supported by a set of castors to bear its weight and enable smooth rotation around the central axis. The extrusion frame is equipped with adjustable camera mounts, allowing DSLR cameras to be positioned flexibly to optimize the capture setup. For our capture process, we utilized three DSLR cameras to perform a 360-degree rotation around the object, capturing images at 9-degree intervals, resulting in 120 photos per object. To ensure precise camera pose estimation, a ChArUco board
+
+![](images/1a6ce4a894ebbfcfb6ec2630ff256afe74443ffa2f522328986bb4e235917f94.jpg)  
+Figure 6. DSLR rig for capturing evaluation data.
+
+was placed beneath the object during the capture. Example images from this setup are shown in Fig. 6.
+
+Environment Maps. Following a similar approach in Stanford-ORB [39], we capture the two environment maps using chrome ball images obtained with the capture rig described earlier. With precise camera poses provided by a ChArUco board placed beneath the chrome ball, we first fit a synthetic 3D sphere to the chrome ball by optimizing its 3D position using a geometry-friendly differentiable renderer [40, 75]. Subsequently, using a differentiable Monte Carlo-based renderer [32], we refine the environment map to match the reflection on the chrome ball, employing the single-view light estimation method proposed in [78]. The coordinate system of the environment map is determined by the ChArUco detection.
+
+Pose Registration for Camera and Object. We first obtain the initial camera poses using the ChArUco board. In most cases, for images captured from the top and middle views, the pose estimates are typically accurate. However, for bottom-view images, inaccuracies arise due to pattern distortion at grazing angles. To mitigate this issue, we refine the camera poses by fitting the rendering of a virtual ChArUco board to the real captured photo using a differentiable renderer [32, 40, 75]. Once the camera poses have been accurately refined, we optimize the object pose by minimizing the mask loss between the rendered mask and the reference one generated by [62]. By providing separate poses for camera and object anchored by ChArUco, the cameras and object are automatically aligned with the optimized environment maps.
+
+# 3.4. Egocentric Evaluation Data
+
+We include an evaluation dataset of real world recordings captured by an egocentric device paired with 100 objects from the DTC dataset. We capture the egocentric recordings using the open-sourced Project Aria device [22] and acquire the additional 3D ground truth using its machine perception tool, which includes online device calibration, device trajectory and semi-dense point clouds for each recording. Each recording contains a single 3D object and precisely aligned object poses in the Aria trajectory coordinate frame.
+
+![](images/dcd62f9fc15c847d5a6c0ee8cc41a039480a020f8dc5ae093f19a24eaae0f820.jpg)  
+Figure 7. The workflow to align egocentric video and 3D objects. We acquire the object's semi-dense point cloud from the egocentric recording and the neural reconstructed mesh using Neural-PBIR [62]. Finally, we align the 3D object with the rendered mask from the neural reconstructed mesh using physics-based differentiable rendering (PBDR).
+
+Both the object and the trajectory are in metric scale. We can derive additional ground truth for each video from the aligned 3D object properties.
+
+Data Capture. To feature real world recordings observed from human perspectives that can be representative of 3D object reconstruction for AR/MR devices or robots, we provide two types of recording trajectories for selected objects, termed active and passive respectively, collected by human wearers. The active recording features a complete 360 view of the objects, which is similar to existing object 3D novel view synthesis dataset. The passive recording features casual looks from human wearer, which only contain partial views of the object from certain viewing angles along the trajectory. In dataset creation, we collected the active and passive recordings in the same environment and generate their 3D information in the shared 3D space. This helps reduces potential failures when aligning the object to passive 3D recordings, which are shorter and contains less 3D information. To reduce the effect of noises and motion blur, which are common in egocentric videos in indoor low light environments, we light the capture environment to  $3\mathrm{K}+$  lux illumination and used a fixed low-exposure and gain profile to collect each recording with the appropriate brightness.
+
+Alignment between Egocentric Video and Object. We provide an illustration of the object alignment to the egocentric video in Fig. 7. Given the images, camera poses and semi-dense point cloud acquired from Project Aria tools, we employ a neural-based mesh reconstruction method [62] to
+
+create reference meshes for generating high-quality reference masks and used that to align with the corresponding 3D object mesh. This alignment step serves as an initialization for a more precise pose refinement, which leverages differentiable rendering. For certain objects with symmetric geometry, we observe this process can introduce ambiguities in point cloud registration and subsequent failures. To address such cases, we provide a GUI to manually align and correct the object alignment. Finally, akin to the DSLR camera pose registration phase, we optimize a mask loss over object poses to achieve fine-tuned pose registration.
+
+# 4. Benchmarking and Applications
+
+We first use our DLSR and egocentric dataset as a benchmark for existing state-of-the-art methods. For inverse rendering, we design metrics to evaluate the shape and material quality of the recovered 3D object digital twin from three perspectives. For egocentric recording, we evaluate the novel-view synthesis as the initial evaluation. We include additional tasks, e.g. sparse view reconstruction in the supplementary materials for both DSLR and egocentric recordings. Finally we can demonstrate our high quality 3D digital twin models can be beneficial to robotics domain using an application in robotics manipulation.
+
+# 4.1. Application to Inverse Rendering for DSLR
+
+The DSLR dataset in DTC provides accurate ground truth, including poses, lighting and 3D models, for inverse rendering
+
+Table 2. Benchmark comparison of existing methods on inverse rendering for DSLR. Depth SI-MSE and Shape Chamfer distance  $\times  {10}^{-3}$  .  
+
+<table><tr><td rowspan="2"></td><td colspan="3">Geometry</td><td colspan="4">Novel Scene Relighting</td><td colspan="4">Novel View Synthesis</td></tr><tr><td>Depth↓</td><td>Normal↓</td><td>Shape↓</td><td>PSNR-H↑</td><td>PSNR-L↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR-H↑</td><td>PSNR-L↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>Neural-PIL [12]</td><td>5.71</td><td>0.25</td><td>25.02</td><td colspan="4">N/A</td><td>28.42</td><td>35.76</td><td>0.882</td><td>0.096</td></tr><tr><td>PhySG [80]</td><td>0.31</td><td>0.16</td><td>11.31</td><td>27.28</td><td>32.86</td><td>0.959</td><td>0.049</td><td>28.54</td><td>34.46</td><td>0.964</td><td>0.045</td></tr><tr><td>NVDiffRec [53]</td><td>0.02</td><td>0.07</td><td>1.64</td><td>26.99</td><td>33.27</td><td>0.951</td><td>0.037</td><td>28.95</td><td>34.92</td><td>0.967</td><td>0.029</td></tr><tr><td>NeRD [11]</td><td>4.55</td><td>0.45</td><td>108.20</td><td>26.10</td><td>32.60</td><td>0.948</td><td>0.061</td><td>26.80</td><td>33.40</td><td>0.882</td><td>0.102</td></tr><tr><td>InvRender [71]</td><td>0.22</td><td>0.03</td><td>0.75</td><td>29.52</td><td>35.98</td><td>0.961</td><td>0.037</td><td>31.64</td><td>37.82</td><td>0.970</td><td>0.033</td></tr><tr><td>NVDiffRecMC [29]</td><td>0.02</td><td>0.06</td><td>1.34</td><td>27.78</td><td>34.55</td><td>0.952</td><td>0.042</td><td>31.27</td><td>38.17</td><td>0.972</td><td>0.032</td></tr></table>
+
+Table 3. Benchmark on the egocentric aligned recordings.  
+
+<table><tr><td></td><td>PSNR ↑</td><td>LPIPS ↓</td><td>SSIM ↑</td><td>Depth ↓</td><td>Normal ↓</td></tr><tr><td>3D-GS [37]</td><td>28.81</td><td>0.020</td><td>0.9888</td><td>0.1768</td><td>0.3301</td></tr><tr><td>2D-GS [31]</td><td>28.75</td><td>0.020</td><td>0.9886</td><td>0.1755</td><td>0.2112</td></tr></table>
+
+tasks and serves as an evaluation suite to benchmark the performance of inverse rendering methods. We select six prior methods for this task and evaluate their performance using the ground truth provided by our dataset. In the following sections, we describe the data splitting strategy, evaluation metrics, and baselines.
+
+Data Splitting. For benchmarking purposes, we select 15 objects from the DSLR dataset captured under two distinct lighting environments, resulting in a total of 30 image sequences. The selected objects encompass a diverse range of geometric and material properties to ensure a comprehensive evaluation. For each scene, 8 views are selected for testing, while the remaining views are reserved for training.
+
+Evaluation Metrics. The metrics measure the accuracy of three aspects of baseline performance: geometry estimation, relighting, and novel view synthesis. For geometry estimation, we evaluate the accuracy of predicted depth and normal maps under held-out test views, as well as 3D meshes extracted from baseline methods, compared with the ground truth from our dataset. Relighting metrics evaluate the material decomposition quality of baselines by measuring the accuracy of predicted images under held-out lighting conditions. For view synthesis, we compare the predicted images from viewpoints unseen during training to ground truth captures. We refer to Kuang et al. [39] for metric details.
+
+Baselines. We include the following baselines: NVDiffRec [53] and NVDiffRecMC [29], with a hybrid shape representation DMTet [60]; InvRender [85] and PhySG [80], which adopt signed distance functions (SDFs) to represent object geometry [76] and utilize implicit neural fields for material decomposition; Neural-PIL [12] and NeRD [11], which use NeRFs [52] as scene representations.
+
+# 4.2. Application to Egocentric Reconstruction
+
+Our digital twin models, aligned with real world video using the method described in Sec. 3.4, can help obtain accurate
+
+ground truth for object-centric images that were previously difficult to acquire. We provide the first evaluation of object-centric novel view synthesis recorded from an egocentric device. We use the projected object shape given the 3D pose of the object and cameras in scene coordinates to acquire the image masks, depth and normal for each object. We selected 15 recordings from the egocentric recording sessions as the evaluation and used the active recordings to benchmark novel view reconstruction. For each recording, we hold out every 8th image view as a testing view.
+
+**Evaluations.** We build our baselines based on the gsplats [77] implementation of the 3D Gaussian Splitting (GS) [37] and 2D GS [31], and handle the effect of lens shading from the Project Aria lens [26]. We calculate PSNR, depth and normal based on the observed objects with masks and provide SSIM and LPIPS score on images by masking out the non-object areas as black. Table 3 shows the benchmark results of the baselines. We use the same depth and normal metric in DSLR evaluation. We provide additional qualitative evaluations and analyses on egocentric data towards sparser view settings in the supplementary materials.
+
+# 4.3. Application to Robotic Manipulation
+
+High-quality object models have been leveraged in prior work to train real-world robotic agents in scenes represented explicitly [54] or implicitly [64]. These object models have also been shown to facilitate object-centric pose and lighting parameter estimation, enabling model-based planning [63]. In this section, we empirically evaluate the effectiveness of using DTC dataset objects in training robotic policies. Specifically, we consider learning robotic pushing and grasping skills in simulation.
+
+First, we sample a subset of 24 cup category objects from the DTC dataset and 24 cup objects from Objaverse-XL [19]  ${}^{1}$  . Since not all Objverse-XL objects come with textures, we randomize the colors of those objects uniformly in RGB space. To compute collision meshes for physical simulation, we perform convex decomposition on each object with CoACD [68]. We import these objects along with a UR5e robot equipped with a Robotiq 2F-85 (pushing) or
+
+<table><tr><td>Task</td><td>DTC (ours)</td><td>Objverse-XL [19]</td></tr><tr><td>Pushing @ 2cm</td><td>36.3% ± 1.5%</td><td>25.3% ± 6.0%</td></tr><tr><td>Pushing @ 3cm</td><td>43.7% ± 1.2%</td><td>29.7% ± 6.0%</td></tr><tr><td>Pushing @ 5cm</td><td>47.0% ± 2.6%</td><td>40.3% ± 5.5%</td></tr><tr><td>Grasping</td><td>42.7% ± 4.7%</td><td>38.6% ± 11.0%</td></tr></table>
+
+Table 4. Success rate of policies trained on data collected using objects from our DTC dataset and sampled from Objaverse-XL when evaluated on an unseen test object. Errors indicate sample standard deviation over three policy training seeds.
+
+Robotiq 2F-140 (grasping) gripper into the PyBullet simulator [17] and collect data for each robotic task as described below. After training policies on data from each object set, we evaluate policy performance on a relatively high-quality unseen test object from the StanfordORB dataset [39].
+
+Pushing. For the pushing task, we collect 5000 trajectories of pseudo-random robotic interaction data for each object set. For each trajectory, a single object from the considered object set and its initial position are randomly selected. Then we train a goal-conditioned neural network policy  $\pi (a|o,o_g)$  where  $o$  is an image observation of the current scene and  $o_{g}$  is a goal image indicating the desired final object and robot position,  $o,o_{g}\in \mathbb{R}^{256\times 256\times 3}$ , and the action  $a\in \mathbb{R}^2$  represents a change in the robot's end-effector position in the  $x$  and  $y$  axes. The  $z$  axis end-effector height is held fixed. We sample goals for training via hindsight relabeling [4, 20, 24]. We then perform evaluation on 100 randomly sampled test goals manipulating an unseen test cup from StanfordORB [39].
+
+Grasping. For grasping, we collect 5000 successful grasp examples for each object set by first placing a single object into the scene, randomizing the object identity and initial position. We then randomly sample candidate grasp poses in a radius around the object's position and simulating their outcomes, rejecting unsuccessful grasps. We train a grasping policy  $\pi(a|o)$  where  $o \in \mathbb{R}^{256 \times 256 \times 3}$  is an image observation of the scene and  $a \in \mathbb{R}^4$  represents the  $x, y, z$  position and  $\theta$  yaw rotation of the robot end-effector at which to attempt the grasp. Again we use 100 test cup object poses.
+
+Results. We report the results in Table 4 and Fig. 8. We find that across both pushing and grasping tasks, policies trained on DTC dataset objects outperform those trained on Objaverse-XL objects when evaluated on the unseen test object. For pushing, we report performance by defining binary success thresholds based on the final Euclidean distance of the object position to the goal position. Training on DTC objects appears to be especially helpful at enabling policies to make finer adjustments, improving pushing success rates at stricter thresholds. Additional experimental details can be found in the supplementary.
+
+![](images/3b4d8b3f2caaf2fc9858feb7baa824272d8d29f523c49ef5c6ccb9d47ac20594.jpg)  
+Figure 8. Success rates on robotic pushing task when training with our DTC objects and sampled Objaverse-XL objects. Particularly at lower error thresholds, policies trained on DTC objects outperform those trained using Objaverse-XL objects. Shaded bars represent sample standard deviations over policy training random seeds.
+
+# 5. Conclusion
+
+We presented a new large scale photorealistic 3D digital twin dataset with the real world recordings that contain its real world counterpart. We provide extensive evaluations of baselines on our DTC dataset serving as new benchmark for inverse rendering and novel view synthesis task. We also demonstrated that high quality digital twin models can be beneficial to applications in robotics domain. We believe our efforts can empower the research community to build and leverage digital twin models for future applications.
+
+Limitations. Achieving high quality digital twin models currently requires deliberate hardware setup and human efforts in refinement. Solving this challenge without sacrificing quality can significantly further enhance the volume of digital twin models. Our hardware is also limited to objects within a certain size and can not yet recover objects that are deformable, highly specular, or transparent.
+
+Future work. The existing digital twin model creation in DTC dataset involves lengthy post-processing and may require subjective human refinement, hindering the automation of model generation. However, recent advancements in physics-based differentiable rendering hold promise for enabling faster and more accurate creation of digital twins, especially for material reconstruction. Furthermore, building large-scale digital twins for applications will necessitate efforts to enhance the diversity in object appearance (e.g., transparent objects) and to capture additional attributes, such as physical properties and functionalities.
+
+For robotics applications, while deploying manipulation policies learned in simulation to the real world remains generally challenging, we hope that the high-quality digital twin data provided by DTC can serve as a stepping stone towards effective sim-to-real transfer.
+
+Acknowledgments. This work is in part supported by NSF CCRI #2120095, RI #2211258, and RI #2338203. YZ is in part supported by the Stanford Interdisciplinary Graduate Fellowship.
+
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2025/Dinomaly_ The Less Is More Philosophy in Multi-Class Unsupervised Anomaly Detection/269a00de-90dc-4a5c-8e52-737661810fb4_content_list.json

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+        "text": "Dinomaly: The Less Is More Philosophy in Multi-Class Unsupervised Anomaly Detection",
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+        "text": "Jia Guo $^{1}$  Shuai Lu $^{2}$  Weihang Zhang $^{2\\dagger}$  Fang Chen $^{3}$  Huiqi Li $^{2\\dagger}$  Hongen Liao $^{1,3\\boxtimes}$",
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+        "text": "$^{1}$ School of Biomedical Engineering, Tsinghua University, Beijing, China  $^{2}$ Beijing Institute of Technology, Beijing, China",
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+        "text": "guojia.jeremy@gmail.com lushuaie@163.com zhangweihang@bit.edu.cn chen-fang@sjtu.edu.cn huiqili@bit.edu.cn liao@tsinghua.edu.cn",
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+        "text": "Abstract",
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+        "text": "Recent studies highlighted a practical setting of unsupervised anomaly detection (UAD) that builds a unified model for multi-class images. Despite various advancements addressing this challenging task, the detection performance under the multi-class setting still lags far behind state-of-the-art class-separated models. Our research aims to bridge this substantial performance gap. In this paper, we present Dinomaly, a minimalist reconstruction-based anomaly detection framework that harnesses pure Transformer architectures without relying on complex designs, additional modules, or specialized tricks. Given this powerful framework consisting of only Attentions and MLPs, we found four simple components that are essential to multi-class anomaly detection: (1) Scalable foundation Transformers that extracts universal and discriminative features, (2) Noisy Bottleneck where pre-existing Dropouts do all the noise injection tricks, (3) Linear Attention that naturally cannot focus, and (4) Loose Reconstruction that does not force layer-to-layer and point-by-point reconstruction. Extensive experiments are conducted across popular anomaly detection benchmarks including MVtec-AD, VisA, Real-IAD, etc. Our proposed Dinomaly achieves impressive image-level AUROC of  $99.6\\%$ ,  $98.7\\%$ , and  $89.3\\%$  on the three datasets respectively, which is not only superior to state-of-the-art multi-class UAD methods, but also achieves the most advanced class-separated UAD records. Code is available at: https://github.com/guojiajeremy/Dinomaly",
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+        "text": "1. Introduction",
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+        "text": "Unsupervised anomaly detection (UAD) aims to detect abnormal patterns from normal images and further localize the anomalous regions. Because of the diversity of potential anomalies and their scarcity, this task is proposed to model the accessible training sets containing only normal samples as an unsupervised paradigm. UAD has a wide range of applications, e.g., industrial defect detection [3], medical disease screening [13], and video surveillance [37], addressing the difficulty of collecting and labeling all possible anomalies in these scenarios.",
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+        "text": "Conventional works on UAD build a separate model for each object category, as shown in Figure 1(a). However, this one-class-one-model setting entails substantial storage overhead for saving models [60], especially when the application scenario necessitates a large number of object classes. For UAD methods, a compact boundary of normal patterns is vital to distinguish anomalies. Once the intra-normal patterns become exceedingly complicated due to various classes, the corresponding distribution becomes challenging to measure, consequently harming the detection performance. Recently, UniAD [60] and successive studies have been proposed to train a unified model for multi-class anomaly detection (MUAD), as shown in Figure 1(b). Under this setting, the \"identity mapping\" that directly copies the input as the output regardless of normal or anomaly harms the performance of conventional methods [60]. This phenomenon is caused by the diversity of multi-class normal patterns that drive the network to generalize on unseen patterns.",
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+        "text": "Within two years, a number of methods have been proposed to address MUAD, such as neighbor-masked attention [60], synthetic anomalies [68], vector quantization [36], diffusion model [16, 59], and state space model (Mamba) [17]. However, there is still a non-negligible per",
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+        "text": "CVF",
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+    {
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "Corresponding author. † Former advisors when the project initiated.",
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+        "text": "20405",
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+        "image_caption": [
+            "(a) Class-Separated UAD Setting"
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+            "Real-IAD (30 classes)"
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+        "image_caption": [
+            "(b)",
+            "Model-Unified",
+            "Multi-Class UAD Setting"
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+        "image_caption": [
+            "(d) Scaling Properties of Dinomaly on MVTec-AD.  $\\dagger$  : default setting."
+        ],
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+        "image_caption": [
+            "(c) Image-Level AUROC on 3 Benchmarks"
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+        "image_caption": [
+            "Figure 1. Setting, benchmarking, and scaling of Dinomaly. (a) Task setting of class-separated UAD. (b) Task setting of MUAD. (c) Comparison with previous SoTA methods on MVtec-AD [3], VisA [70], and Real-IAD [54]. (d) Scaling properties of Dinomaly."
+        ],
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+    {
+        "type": "text",
+        "text": "formance gap between the state-of-the-art (SoTA) MUAD methods and class-separated UAD methods, restricting the practicability of implementing unified models, as shown in Figure 1(c). In addition, previous methods employ modules and architectures delicately designed, which may not be straightforward, and consequently suffer from limited universality and ease-of-use [18, 36].",
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+    {
+        "type": "text",
+        "text": "In this work, we aim to catch up with the performance of class-separated anomaly detection models using a multiclass unified model. We introduce Dinomaly, a minimalist reconstruction-based UAD framework built exclusively by pure Transformer blocks [51], specifically Self-Attentions and Multi-Layer Perceptrons (MLPs). To begin with, we empirically investigate the scaling law of self-supervised pre-trained Vision Transformers (ViT) [12] when serving as the feature encoders for extracting reconstruction objectives. Subsequently, we introduce three straightforward yet crucial elements to address the critical identity mapping phenomenon in MUAD contexts, without increasing complexity or computational burden. First, as an alternative to meticulously designed pseudo anomaly and feature noise, we propose to activate the built-in Dropout in an MLP to prevent the network from restoring both normal and anomalous patterns. Second, we propose to leverage the \"side effect\" of Linear Attention (a computation-efficient counterpart of Softmax Attention) that impedes focus on local regions, thus preventing the forwarding of identical information. Third, previous methods adopt layer-to-layer and region-by-region reconstruction schemes, distilling a decoder that can well mimic the encoder's behavior even for anomalous regions. Therefore, we propose to loosen the reconstruction constraints by grouping multiple layers as a",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "whole and discarding well-reconstructed regions during optimization.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To validate the effectiveness of the proposed Dinomaly under MUAD setting, we conduct extensive experiments on a number of widely used benchmarks, including MVTec AD [3] (15 classes), VisA [70] (12 classes), and RealIAD (30 classes). As shown in Figure 1, our base-size Dinomaly achieves unprecedented image-level AUROC of  $99.6\\%$ ,  $98.7\\%$ , and  $89.3\\%$  on MVTec AD, VisA, and RealIAD, surpassing previous SoTA methods by a large margin. In addition, scalability is a key feature of Dinomaly. Further scaling up the model size maximizes performance to the fullest level of  $99.8\\%$ ,  $98.9\\%$ , and  $90.1\\%$ , respectively; while scaling down parameters and input size can offer efficient solutions in computation-constrained scenarios.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Multi-Class UAD. UniAD [60] first introduced multi-class anomaly detection, aiming to detect anomalies for different classes using a unified model. In this setting, conventional UAD methods often face the challenge of \"identical shortcuts\", where both anomaly-free and anomaly samples can be effectively recovered during inference [60]. It is believed that this phenomenon is caused by the diversity of multi-class normal patterns that drive the network to generalize on unseen patterns. This contradicts the fundamental assumption of epistemic methods. Many current researches focus on addressing this challenge [14, 31, 36, 59, 60]. UniAD [60] employs a neighbor-masked attention module and a feature-jitter strategy to mitigate these shortcuts. HVQ-Trans [36] proposes a vector quantization (VQ) Transformer model that induces large feature discrepancies",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "20406",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/17d3d0fa6c8cb95057e7196ca865d09815a7ac4253dda8c3a5682950e09bd3d4.jpg",
+        "image_caption": [
+            "Figure 2. The framework of Dinomaly, built by simple and pure Transformer building blocks."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            94,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "for anomalies. LafitE [59] utilizes a latent diffusion model and introduces a feature editing strategy to alleviate this issue. DiAD [16] also employs diffusion models to address multi-class UAD settings. OmniAL [68] focuses on anomaly localization in the unified setting, preventing identical reconstruction by using synthesized pseudo anomalies. ReContrast [14] attempted to alleviate the identity mapping by cross-reconstruction between two encoders. ViTAD [5] abstracts a unified feature-reconstruction UAD framework and employ Transformer building blocks. MambaAD [17] explores the recently proposed State Space Model (SSM), Mamba, in the context of multi-class UAD. More related works of UAD are presented in Appendix A.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Dinomaly Framework",
+        "text_level": 1,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "\"What I cannot create, I do not understand\"",
+        "bbox": [
+            91,
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+            612
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Richer Feynman",
+        "bbox": [
+            109,
+            614,
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+            628
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The ability to recognize anomalies from what we know is an innate human capability, serving as a vital pathway for us to explore the world. Similarly, we construct a reconstruction-based framework that relies on the epistemic characteristic of artificial neural networks. Dinomaly consists of an encoder, a bottleneck, and a reconstruction decoder, as shown in Figure 2. Without loss of generality, a pretrained ViT network [12] with 12 Transformer layers is used as the encoder, extracting informative feature maps with different semantic scales. The bottleneck is a simple MLP (a.k.a. feed-forward network, FFN) that collects the feature representations of the encoder's 8 middle-level layers. The decoder is similar to the encoder, consisting of 8 Transformer layers. During training, the decoder learns to reconstruct the middle-level features of the encoder by maximizing the cosine similarity between feature maps. During inference, the decoder is expected to reconstruct normal regions of feature maps but fails for anomalous regions as it",
+        "bbox": [
+            89,
+            628,
+            485,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "has never seen such samples.",
+        "bbox": [
+            511,
+            342,
+            705,
+            356
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Foundation Transformers. Foundation models, especially ViTs [12, 33] pre-trained on large-scale datasets, serve as a basis and starting point for specific computer vision tasks. Such networks employ self-supervised learning schemes such as contrastive learning (MoCov3 [6], DINO [4]), masked image modeling (MAE [19], SimMIM [57], BEiT [40]), and their combination (iBOT [69], DINOv2 [39]), producing universal features suitable for image-level visual tasks and pixel-level visual tasks.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Because of the lack of supervision in UAD, most advanced methods adopt pre-trained networks to extract discriminative features. Recent works [28, 43, 65] have preliminarily discovered the advantage of robust and universal features of self-supervised models over domain-specific ImageNet features in anomaly detection tasks. In this paper, we pioneer the investigation of scaling behaviors in UAD models through a systematic analysis of foundational ViTs, as briefed in Figure 1(d). Our comprehensive evaluation encompasses pre-training strategies (Figure 5), model sizes (Table 4), and input resolutions (Table 5), which are detailed in section 4.4. Considering the balance of detection performance and computational efficiency, we adopt ViT-Base/14 pretrained by DINoV2-Register [7] as the encoder of Dinomaly by default.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Noisy Bottleneck.",
+        "text_level": 1,
+        "bbox": [
+            511,
+            726,
+            684,
+            742
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "\"Dropout is all you need.\"",
+        "bbox": [
+            513,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Prior studies [14, 60, 68] attribute the performance degradation of UAD methods trained on diverse multi-class samples to the \"identity mapping\" phenomenon; in this work, we reframe this issue as an \"over-generalization\" problem. Generalization ability is a merit of neural networks, allowing them to perform equally well on unseen test sets. However, generalization is not so wanted in the context of unsupervised anomaly detection that leverages the epistemic nature of neural networks. With the increas",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "20407",
+        "bbox": [
+            478,
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+            519,
+            957
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6d4a43b73593602e9e9d33bb1e07ed954c2eb370106d46e6efa33d5071ffbc4f.jpg",
+        "image_caption": [
+            "Figure 3. Softmax Attention vs. Linear Attention. (a) Visualization of attention maps. (b) Attention distribution."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            158,
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+            340
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/8d125b0bc5327cd9d9792b71ec97f6b7783286bcb1c5a99b13be4c2f135ca734.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ing diversity of images and their patterns due to multi-class UAD settings, the decoder can generalize its reconstruction ability to unseen anomalous samples, resulting in the failure of anomaly detection using reconstruction error.",
+        "bbox": [
+            88,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A direct solution for identity mapping is to shift \"reconstruction\" to \"restoration\". Specifically, instead of directly reconstructing the normal images or features given normal inputs, previous works propose to add perturbations as pseudo anomalies on input images [62, 67] or on encoder features [59, 60]; meanwhile, still let the decoder restore anomaly-free images or features, formulating a denoising-like framework. However, such methods employ heuristic and hand-crafted anomaly generation strategies that may not be universal across domains, datasets, and methods. In this work, we turn to leveraging the simple and elegant Dropout techniques. Since its introduction by Hinton et al. [21] in 2014 as a remedy for overfitting, Dropout has become a cornerstone element in neural architectures, including Transformers. In Dinomaly, we employ Dropout to randomly discard neural activations in an MLP bottleneck. Instead of alleviating overfitting, the role of Dropout in Dinomaly can be explained as pseudo feature anomaly that perturb normal representations, analogous to denoising auto-encoders [52, 53]. Without introducing any specific modules, this simple component inherently forces the decoder to restore normal features regardless of whether the test image contains anomalies, in turn, mitigating identical mapping.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Unfocused Linear Attention.",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "\"One man's poison is another man's meat\"",
+        "bbox": [
+            91,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Softmax Attention is the key mechanism of Transformers, allowing the model to attend to different parts of its",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "input token sequence. Formally, given an input sequence  $\\mathbf{X} \\in \\mathbb{R}^{N \\times d}$  with length  $N$ , Attention first transforms it into three matrices: the query matrix  $\\mathbf{Q} \\in \\mathbb{R}^{N \\times d}$ , the key matrix  $\\mathbf{K} \\in \\mathbb{R}^{N \\times d}$ , and the value matrix  $\\mathbf{V} \\in \\mathbb{R}^{N \\times d}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Q} = \\mathbf {X} \\mathbf {W} ^ {Q}, \\mathbf {K} = \\mathbf {X} \\mathbf {W} ^ {K}, \\mathbf {V} = \\mathbf {X} \\mathbf {W} ^ {V}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            568,
+            469,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}^Q, \\mathbf{W}^K, \\mathbf{W}^V \\in \\mathbb{R}^{d \\times d}$  are learnable parameters. By computing the attention map by the query-key similarity, the output of Softmax Attention is given as:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} (\\mathbf {Q K} ^ {T}) \\mathbf {V}. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Back to MUAD, previous methods [36, 60] suggest adopting Attentions instead of Convolutions because Convolutions can easily learn identical mappings. Nevertheless, both operations are in danger of forming identity mapping by over-concentrating on corresponding input locations for producing the outputs:",
+        "bbox": [
+            511,
+            590,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {C o n v} \\operatorname {K e r n e l} = \\left[ \\begin{array}{l l l} 0 & 0 & 0 \\\\ 0 & 1 & 0 \\\\ 0 & 0 & 0 \\end{array} \\right], \\quad \\operatorname {A t t n} \\operatorname {M a p} = \\left[ \\begin{array}{l l l} 1 & 0 & 0 \\\\ 0 & 1 & 0 \\\\ 0 & 0 & 1 \\end{array} \\right].\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            693,
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+            743
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Is there any simple solution that prevents Attentions from attending to identical information? In Dinomaly, we turn to leverage the \"unfocusing ability\" of a type of Softmax-free Attention, i.e., Linear Attention. Linear Attention was proposed as a promising alternative to reduce the computation complexity of vanilla Softmax Attention",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>The full form of Attention is Softmax  $\\left(\\frac{\\mathbf{Q}\\mathbf{K}^T}{\\sqrt{d}}\\right)\\mathbf{V}$ . The constant denominator is omitted for narrative simplicity. The multi-head mechanism that concatenates multiple Attentions is also omitted.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "footer",
+        "text": "20408",
+        "bbox": [
+            478,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/a1dd9fa401691a462a4df3a84a2f8feedcaf54499e447957f60fb2c121c62204.jpg",
+        "image_caption": [
+            "(a) layer-to-layer sparse"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            106,
+            89,
+            233,
+            185
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/b866424b103ff548ef2ecbe121963fe58d37f24999027884bb87e659c5bc10ba.jpg",
+        "image_caption": [
+            "(b) layer-to-cat-layer"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            251,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/b4bffa389b2c5780fbe925887470053347f3965c3cfab98e72337e6b9155bdfe.jpg",
+        "image_caption": [
+            "(c) layer-to-layer dense"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            395,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/2e691d240b522deeace347316f62ed4982cc6efcf42bc8289ce3948972a78386.jpg",
+        "image_caption": [
+            "(d) group-to-group 1 group (Ours)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            534,
+            87,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/0302c001c32f5d638e646b4c5b0696ae395e2e4637f8de43dad4b5752f96a3ad.jpg",
+        "image_caption": [
+            "(e) group-to-group 2 group (Ours)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            671,
+            88,
+            774,
+            181
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/d3bc1adf7c570b9343648410728143a6c2329294536bf9af7d61d3b9329c354d.jpg",
+        "image_caption": [
+            "encoder feature"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            815,
+            95,
+            836,
+            114
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/4767d4991e7ce4e01a71213986c2b2383e2a08849f258d4d882d31d17534b15e.jpg",
+        "image_caption": [
+            "decoder feature"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            816,
+            125,
+            836,
+            138
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/f33596ba1387f7c0a6e5d9120039352aced6c9d016bf983caf8f1150221ea210.jpg",
+        "image_caption": [
+            "reconstruct"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            816,
+            147,
+            836,
+            155
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/c37867f60176995bbf10bf74c757ea2ab30dd85d912f29e92525a9a0297ad90e.jpg",
+        "image_caption": [
+            "concatenate"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            816,
+            162,
+            836,
+            172
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/ac76c81cae97fc845173fcf13a54643878bec7b040506ee9b893173e98d3134b.jpg",
+        "image_caption": [
+            "add",
+            "Figure 4. Schemes of reconstruction constraint. (a) Layer-to-layer (sparse). (b) Layer-to-cat-layer. (c) Layer-to-layer (dense). (d) Loose group-to-group, 1-group (Ours). (e) Loose group-to-group, 2-group (Ours)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            816,
+            178,
+            836,
+            186
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "concerning the number of tokens [26]. By substituting Softmax operation with a simple activation function  $\\phi (\\cdot)$  (usually  $\\phi (x) = \\mathrm{elu}(x) + 1$ ), we can change the computation order from  $(\\mathbf{Q}\\mathbf{K}^T)\\mathbf{V}$  to  $\\mathbf{Q}(\\mathbf{K}^T\\mathbf{V})$ . Formally, Linear Attention (LA) is given as:",
+        "bbox": [
+            88,
+            273,
+            483,
+            349
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {L A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = (\\phi (\\mathbf {Q}) \\phi \\left(\\mathbf {K} ^ {T}\\right)) \\mathbf {V} = \\phi (\\mathbf {Q}) \\left(\\phi \\left(\\mathbf {K} ^ {T}\\right) \\mathbf {V}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            354,
+            483,
+            386
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the computation complexity is reduced to  $\\mathcal{O}(Nd^2)$  from  $\\mathcal{O}(N^2 d)$ . The trade-off between complexity and expressiveness is a dilemma. Previous studies [15, 48] attribute Linear Attention's performance degradation on supervised tasks to its incompetence in focusing. Due to the absence of non-linear attention reweighting by Softmax operation, Linear Attention cannot concentrate on important regions related to the query, such as foreground and neighbors. This property, however, is exactly what the reconstruction decoder favors in our contexts.",
+        "bbox": [
+            88,
+            386,
+            483,
+            537
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In order to probe how Attentions propagate information, we train two variants of Dinomaly using vanilla Softmax Attention or Linear Attention as the spatial mixer in the decoder and visualize their attention maps. As shown in Figure 3, Softmax Attention tends to focus on the exact region of the query, while Linear Attention spreads its attention across the whole image. This implies that Linear Attention, forced by its incompetence to focus, utilizes more long-range information to restore features at each position, reducing the chance of passing identical information of unseen patterns to the next layer during reconstruction. Of course, employing Linear Attention also benefits from less computation, free of performance drop.",
+        "bbox": [
+            88,
+            537,
+            483,
+            733
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Loose Reconstruction",
+        "text_level": 1,
+        "bbox": [
+            89,
+            742,
+            294,
+            756
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "\"The tighter you squeeze, the less you have.\"",
+        "bbox": [
+            91,
+            763,
+            388,
+            779
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Loose Constraint. Pioneers of feature-reconstruction/distillation UAD methods [10, 46] are inspired by knowledge distillation [20]. Most reconstruction-based methods distill specific encoder layers (e.g. 3 last layers of 3 ResNet stages) by the corresponding decoder layers [10, 46, 65] (Figure 4(a)) or the last decoder layer [58, 60] (Figure 4(b)). Intuitively, with more encoder-decoder feature pairs (Figure 4(c)), UAD model can utilize",
+        "bbox": [
+            88,
+            779,
+            483,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "more information in different layers to discriminate anomalies. However, according to the intuition of knowledge distillation, the student (decoder) can better mimic the behavior of the teacher (encoder) given more layer-to-layer supervision [30], which is harmful for UAD models that detect anomalies by encoder-decoder discrepancy. This phenomenon is also embodied as identity mapping. Thanks to the top-to-bottom consistency of columnar Transformer layers, we propose to loosen the layer-to-layer constraint by adding up all feature maps of interested layers as a whole group, as shown in Figure 4(d). This scheme can be seen as loosening the layer-to-layer correspondence and providing the decoder with more degrees of freedom, so that the decoder is allowed to act much more differently from the encoder when the input pattern is unseen. Because features of shallow layers contain low-level visual characters that are helpful for precise localization, we can further group the features into the low-semantic-level group and high-semantic-level group, as shown in Figure 4(e).",
+        "bbox": [
+            511,
+            273,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "**Loose Loss.** Following the above analysis, we also loosen the point-by-point reconstruction loss function by discarding some points in the feature map. Here, we simply borrow the hard-mining global cosine loss [14] that detaches the gradients of well-restored feature points with low cosine distance during training. Let  $f_{E}$  and  $f_{D}$  denotes (grouped) feature maps of encoder and decoder:",
+        "bbox": [
+            511,
+            560,
+            908,
+            666
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {g l o b a l} - h m} = \\mathcal {D} _ {\\text {c o s}} \\left(\\mathcal {F} \\left(f _ {E}\\right), \\mathcal {F} \\left(\\hat {f} _ {D}\\right)\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            584,
+            674,
+            903,
+            691
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {f} _ {D} (h, w) = \\left\\{ \\begin{array}{l} s g \\left(f _ {D} (h, w)\\right)_{0.1}, \\text {if} \\mathcal {D} _ {\\text {cos}} \\left(f _ {D}, f _ {E}\\right) <   k \\% _ {\\text {batch}} \\\\ f _ {D} (h, w), \\text {else} \\end{array} \\right. \\tag{5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            699,
+            903,
+            739
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\cos} (a, b) = 1 - \\frac {a ^ {T} \\cdot b}{\\| a \\| \\| b \\|}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            622,
+            739,
+            903,
+            770
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{D}_{cos}$  denotes cosine distance,  $\\mathcal{F}(\\cdot)$  denotes flatten operation,  $f_{D}(h,w)$  represents the feature point at  $(h,w)$ , and  $sg(\\cdot)_{0.1}$  denotes shrink the gradient to one-tenth of the original  $^2$ .  $\\mathcal{D}_{cos}(f_D(h,w),f_E(h,w)) < k\\%_{batch}$  selects  $k \\%$  feature points with smaller cosine distance within a batch for gradient shrinking. Total loss is the average  $\\mathcal{L}_{global - hm}$  of all encoder-decoder feature pairs.",
+        "bbox": [
+            511,
+            772,
+            906,
+            878
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "${}^{2}$  Complete stop-gradient causes optimization instability occasionally.",
+        "bbox": [
+            529,
+            886,
+            897,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "footer",
+        "text": "20409",
+        "bbox": [
+            478,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/63abb526d89a5fc1376c69e0a3620b9eeaa44da1e212790f58926cb7f3502cf6.jpg",
+        "table_caption": [
+            "Table 1. Performance under multi-class UAD setting (%). †: method designed for MUAD. Dinomaly†: training schedule is scaled up to 20,000, 20,000, and 100,000 iterations (original: 10,000/10,000/50,000)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td rowspan=\"2\">Method</td><td colspan=\"3\">Image-level</td><td colspan=\"4\">Pixel-level</td></tr><tr><td>AUROC</td><td>AP</td><td>\\(F_1\\)-max</td><td>AUROC</td><td>AP</td><td>\\(F_1\\)-max</td><td>AUPRO</td></tr><tr><td rowspan=\"10\">MVTec-AD [3]</td><td>RD4AD [10]</td><td>94.6</td><td>96.5</td><td>95.2</td><td>96.1</td><td>48.6</td><td>53.8</td><td>91.1</td></tr><tr><td>SimpleNet [34]</td><td>95.3</td><td>98.4</td><td>95.8</td><td>96.9</td><td>45.9</td><td>49.7</td><td>86.5</td></tr><tr><td>DeSTSeg [67]</td><td>89.2</td><td>95.5</td><td>91.6</td><td>93.1</td><td>54.3</td><td>50.9</td><td>64.8</td></tr><tr><td>UniAD [60]†</td><td>96.5</td><td>98.8</td><td>96.2</td><td>96.8</td><td>43.4</td><td>49.5</td><td>90.7</td></tr><tr><td>ReContrast [14]†</td><td>98.3</td><td>99.4</td><td>97.6</td><td>97.1</td><td>60.2</td><td>61.5</td><td>93.2</td></tr><tr><td>DiAD [18]†</td><td>97.2</td><td>99.0</td><td>96.5</td><td>96.8</td><td>52.6</td><td>55.5</td><td>90.7</td></tr><tr><td>ViTAD [65]†</td><td>98.3</td><td>99.4</td><td>97.3</td><td>97.7</td><td>55.3</td><td>58.7</td><td>91.4</td></tr><tr><td>MambaAD [17]†</td><td>98.6</td><td>99.6</td><td>97.8</td><td>97.7</td><td>56.3</td><td>59.2</td><td>93.1</td></tr><tr><td>Dinomaly (Ours)</td><td>99.6</td><td>99.8</td><td>99.0</td><td>98.4</td><td>69.3</td><td>69.2</td><td>94.8</td></tr><tr><td>Dinomaly†</td><td>99.7</td><td>99.8</td><td>99.2</td><td>98.4</td><td>69.3</td><td>69.2</td><td>94.7</td></tr><tr><td rowspan=\"10\">VisA [70]</td><td>RD4AD [10]</td><td>92.4</td><td>92.4</td><td>89.6</td><td>98.1</td><td>38.0</td><td>42.6</td><td>91.8</td></tr><tr><td>SimpleNet [34]</td><td>87.2</td><td>87.0</td><td>81.8</td><td>96.8</td><td>34.7</td><td>37.8</td><td>81.4</td></tr><tr><td>DeSTSeg [67]</td><td>88.9</td><td>89.0</td><td>85.2</td><td>96.1</td><td>39.6</td><td>43.4</td><td>67.4</td></tr><tr><td>UniAD [60]†</td><td>88.8</td><td>90.8</td><td>85.8</td><td>98.3</td><td>33.7</td><td>39.0</td><td>85.5</td></tr><tr><td>ReContrast [14]†</td><td>95.5</td><td>96.4</td><td>92.0</td><td>98.5</td><td>47.9</td><td>50.6</td><td>91.9</td></tr><tr><td>DiAD [18]†</td><td>86.8</td><td>88.3</td><td>85.1</td><td>96.0</td><td>26.1</td><td>33.0</td><td>75.2</td></tr><tr><td>ViTAD [65]†</td><td>90.5</td><td>91.7</td><td>86.3</td><td>98.2</td><td>36.6</td><td>41.1</td><td>85.1</td></tr><tr><td>MambaAD [17]†</td><td>94.3</td><td>94.5</td><td>89.4</td><td>98.5</td><td>39.4</td><td>44.0</td><td>91.0</td></tr><tr><td>Dinomaly (Ours)</td><td>98.7</td><td>98.9</td><td>96.2</td><td>98.7</td><td>53.2</td><td>55.7</td><td>94.5</td></tr><tr><td>Dinomaly†</td><td>98.9</td><td>99.0</td><td>96.4</td><td>98.8</td><td>53.8</td><td>55.8</td><td>94.5</td></tr><tr><td rowspan=\"10\">Real-IAD [54]</td><td>RD4AD [10]</td><td>82.4</td><td>79.0</td><td>73.9</td><td>97.3</td><td>25.0</td><td>32.7</td><td>89.6</td></tr><tr><td>SimpleNet [34]</td><td>57.2</td><td>53.4</td><td>61.5</td><td>75.7</td><td>2.8</td><td>6.5</td><td>39.0</td></tr><tr><td>DeSTSeg [67]</td><td>82.3</td><td>79.2</td><td>73.2</td><td>94.6</td><td>37.9</td><td>41.7</td><td>40.6</td></tr><tr><td>UniAD [60]†</td><td>83.0</td><td>80.9</td><td>74.3</td><td>97.3</td><td>21.1</td><td>29.2</td><td>86.7</td></tr><tr><td>ReContrast [14]†</td><td>86.4</td><td>84.2</td><td>77.4</td><td>97.8</td><td>31.6</td><td>38.2</td><td>91.8</td></tr><tr><td>DiAD [18]†</td><td>75.6</td><td>66.4</td><td>69.9</td><td>88.0</td><td>2.9</td><td>7.1</td><td>58.1</td></tr><tr><td>ViTAD [65]†</td><td>82.7</td><td>80.2</td><td>73.7</td><td>97.2</td><td>24.3</td><td>32.3</td><td>84.8</td></tr><tr><td>MambaAD [17]†</td><td>86.3</td><td>84.6</td><td>77.0</td><td>98.5</td><td>33.0</td><td>38.7</td><td>90.5</td></tr><tr><td>Dinomaly (Ours)</td><td>89.3</td><td>86.8</td><td>80.2</td><td>98.8</td><td>42.8</td><td>47.1</td><td>93.9</td></tr><tr><td>Dinomaly†</td><td>89.5</td><td>86.9</td><td>80.4</td><td>98.9</td><td>43.3</td><td>47.4</td><td>94.2</td></tr></table>",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            89,
+            563,
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+            580
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
+        "bbox": [
+            89,
+            588,
+            297,
+            606
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. MVtec-AD [3] contains 15 objects (5 texture classes and 10 object classes) with a total of 3,629 normal images as the training set and 1,725 images as the test set (467 normal, 1,258 anomalous). VisA [70] contains 12 objects. Training and test sets are split following the official splitting, resulting in 8,659 normal images in the training set and 2,162 images in the test set (962 normal, 1,200 anomalous). Real-IAD [54] is a large UAD dataset recently released, containing 30 distinct objects. We follow the official splitting that includes all views, resulting in 36,465 normal images in the training set and 114,585 images in the test set (63,256 normal, 51,329 anomalous).",
+        "bbox": [
+            89,
+            612,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Metrics. Following prior works [17, 65], we adopt 7 evaluation metrics. Image-level anomaly detection performance is measured by the Area Under the Receiver Operator Curve (AUROC), Average Precision (AP), and  $F_{1}$  score under optimal threshold  $(F_{1}$ -max). Pixel-level anomaly localization is measured by AUROC, AP,  $F_{1}$ -max and the Area Under the Per-Region-Overlap (AUPRO). The results",
+        "bbox": [
+            89,
+            795,
+            482,
+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "of a dataset is the average of all classes.",
+        "bbox": [
+            511,
+            565,
+            777,
+            579
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. ViT-Base/14 (patchsize=14) pre-trained by DINOv2-R [7] is used as the encoder by default. The drop rate of Noisy Bottleneck is 0.2 by default and increases to 0.4 on the diverse Real-IAD. Loose constraint with 2 groups is employed, and the anomaly map is given by the mean per-point cosine distance of the 2 groups. The input image is first resized to  $448^2$  and then center-cropped to  $392^2$ , so the feature map  $(28^2)$  is large enough for anomaly localization. StableAdamW optimizer [56] with AMSGrad [41] (more stable than AdamW [35] in training) is utilized with  $lr = 2e - 3$ ,  $\\beta = (0.9,0.999)$  and  $wd = 1e - 4$ . The network is trained for 10,000 iterations (steps) on MVTec-AD and VisA, and 50,000 iterations on Real-IAD. Detailed settings are available in Appendix B.",
+        "bbox": [
+            511,
+            580,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison to Multi-Class UAD SoTAs",
+        "text_level": 1,
+        "bbox": [
+            511,
+            801,
+            854,
+            816
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We compare the proposed Dinomaly with the most advanced UAD and MUAD methods [10, 14, 17, 18, 34, 65, 67]. Experimental results are presented in Table 1, where Dinomaly surpasses compared methods by a large margin on all datasets and all metrics. On the most",
+        "bbox": [
+            511,
+            825,
+            905,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "20410",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/cd538305d399bb60a141faeaeca01f08a86dc1a2c840fd10c9d92ee535e6db57.jpg",
+        "table_caption": [
+            "Table 2. Performance under conventional class-separated UAD setting (%). n/a: not available."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">MVTec-AD [3]</td><td colspan=\"3\">VisA [70]</td><td colspan=\"3\">Real-IAD [54]</td></tr><tr><td>I-AUROC</td><td>P-AUROC</td><td>P-AUPRO</td><td>I-AUROC</td><td>P-AUROC</td><td>P-AUPRO</td><td>I-AUROC</td><td>P-AUROC</td><td>P-AUPRO</td></tr><tr><td>Dinomaly (MUAD)</td><td>99.6</td><td>98.4</td><td>94.8</td><td>98.7</td><td>98.7</td><td>94.5</td><td>89.3</td><td>98.8</td><td>93.9</td></tr><tr><td>Dinomaly</td><td>99.7</td><td>99.9</td><td>95.0</td><td>98.9</td><td>98.9</td><td>95.1</td><td>92.0</td><td>99.1</td><td>95.1</td></tr><tr><td>RD4AD [10]</td><td>98.5</td><td>97.8</td><td>93.9</td><td>96.0</td><td>90.1</td><td>70.9</td><td>87.1</td><td>n/a</td><td>93.8</td></tr><tr><td>PatchCore [45]</td><td>99.1</td><td>98.1</td><td>93.5</td><td>94.7</td><td>98.5</td><td>91.8</td><td>89.4</td><td>n/a</td><td>91.5</td></tr><tr><td>SimpleNet [34]</td><td>99.6</td><td>98.1</td><td>90.0</td><td>97.1</td><td>98.2</td><td>90.7</td><td>88.5</td><td>n/a</td><td>84.6</td></tr></table>",
+        "bbox": [
+            133,
+            114,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/a326e4c362788dd358ee23012ebf6b13e0d43aae440ef876896212edf481cee2.jpg",
+        "table_caption": [
+            "Table 3. Ablations of Dinomaly elements on MVTec-AD (%). NB: Noisy Bottleneck. LA: Linear Attention. LC: Loose Constraint (2 groups). LL: Loose Loss. As MVTec-AD has reached saturation, we also present the results on VisA (Table A4)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">NB</td><td rowspan=\"2\">LA</td><td rowspan=\"2\">LC</td><td rowspan=\"2\">LL</td><td colspan=\"3\">Image-level</td><td colspan=\"4\">Pixel-level</td></tr><tr><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUPRO</td></tr><tr><td></td><td></td><td></td><td></td><td>98.41</td><td>99.09</td><td>97.41</td><td>97.18</td><td>62.96</td><td>63.82</td><td>92.95</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>99.06</td><td>99.54</td><td>98.31</td><td>97.62</td><td>66.22</td><td>66.70</td><td>93.71</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>98.54</td><td>99.21</td><td>97.62</td><td>97.20</td><td>62.94</td><td>63.73</td><td>93.09</td></tr><tr><td></td><td></td><td>✓</td><td></td><td>98.35</td><td>99.04</td><td>97.43</td><td>97.10</td><td>61.05</td><td>62.73</td><td>92.60</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>99.03</td><td>99.45</td><td>98.19</td><td>97.62</td><td>64.10</td><td>64.96</td><td>93.34</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>99.27</td><td>99.62</td><td>98.63</td><td>97.85</td><td>67.36</td><td>67.33</td><td>94.16</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>99.50</td><td>99.72</td><td>98.87</td><td>98.14</td><td>68.16</td><td>68.24</td><td>94.23</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>99.52</td><td>99.73</td><td>98.92</td><td>98.20</td><td>68.25</td><td>68.34</td><td>94.17</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>99.57</td><td>99.78</td><td>99.00</td><td>98.20</td><td>67.93</td><td>68.21</td><td>94.50</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>99.60</td><td>99.78</td><td>99.04</td><td>98.35</td><td>69.29</td><td>69.17</td><td>94.79</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "widely used MVTec-AD, Dinomaly produces image-level performance of 99.6/99.8/99.0 (\\%) and pixel-level performance of 98.4/69.3/69.2/94.8, outperforming previous SoTAs by 1.0/0.2/1.2 and 0.7/9.1/7.7/1.6. This result declares that the image-level performance on the MVTec-AD dataset is nearly saturated under the MUAD setting. On the popular VisA, Dinomaly achieves image-level performance of 98.7/98.9/96.2 and pixel-level performance of 98.7/53.2/55.7/94.5, outperforming previous SoTAs by 3.2/2.5/4.2 and 0.2/5.3/5.1/2.6. On the Real-IAD that contains 30 classes, each with 5 camera views, we produce image-level and pixel-level performance of 89.3/86.8/80.2 and 98.8/42.8/47.1/93.9, outperforming previous SoTAs by 3.0/2.2/3.2 and 0.3/4.9/5.4/3.4, indicating our scalability to extremely complex scenarios. Per-class performances and qualitative visualization are presented in Appendix E and F. We also produce superior results on other popular UAD benchmarks, i.e., MPDD [24], BTAD [38], and UniMedical [66], with I-AUROC of 97.2, 95.4, and 84.9, respectively, as shown in Table A13 in Appendix.",
+        "bbox": [
+            88,
+            481,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Comparison to Class-Separated UAD SoTAs",
+        "text_level": 1,
+        "bbox": [
+            89,
+            799,
+            467,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Dinomaly is also compared with class-separated SoTAs, as shown in Table 2. Dinomaly under MUAD setting is comparable to conventional methods [10, 34, 45] that build individual models for each class. On MVTec-AD and VisA, multi-class Dinomaly (first row) is subjected to nearly no",
+        "bbox": [
+            89,
+            824,
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+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "performance drop compared to its class-separated counterpart (second row). On the complicated Real-IAD that involves more classes and views, multi-class Dinomaly suffers a moderate performance drop but is still comparable to class-separated SoTAs.",
+        "bbox": [
+            511,
+            481,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            511,
+            571,
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+            588
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Overall Ablation. We conduct experiments to verify the effectiveness of the proposed elements, i.e., Noisy Bottleneck (NB), Linear Attention (LA), Loose Constraint (LC), and Loose Loss (LL). The already-powerful baseline (first row) is Dinomaly with noiseless MLP bottleneck, Softmax Attention, dense layer-to-layer supervision, and global cosine loss. This baseline is very similar to ViTAD [64] and the ViT version of RD4AD [10]. Results on MVtec-AD and VisA are shown in Table 3 and Table A4, respectively. NB and LL can directly contribute to the model performance. LA and LC boost the performance with the presence of NB. The use of LC is not solely beneficial because LC makes the reconstruction too easy without injected noise.",
+        "bbox": [
+            511,
+            595,
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+            792
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Model Scalability. Previous works [10, 60, 65] reported that anomaly detection networks do not follow the \"scaling law\". For example, RD4AD [10] found WideResNet50 better than WideResNet101 as the encoder backbone. ViTAD [65] found ViT-Small better than ViT-Base. On the contrary, as shown in Table 4, the performance of the proposed Dinomaly benefits from scaling. Dinomaly equipped with ViT",
+        "bbox": [
+            511,
+            795,
+            908,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "20411",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/be8fcebda125d516609706bb55b352c692dfdd1fd3e340fc1f33ba3d0c6c7ba7.jpg",
+        "table_caption": [
+            "Table 4. Scaling of ViT model sizes on MVtec-AD (%). Im/s (Throughoutput, image per second) is measured on NVIDIA RTX3090 with batch size=16. Results on VisA and Real-IAD are shown in Table A3. †:default."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Arch.</td><td rowspan=\"2\">Params</td><td rowspan=\"2\">MACs</td><td rowspan=\"2\">Im/s</td><td colspan=\"3\">Image-level</td><td colspan=\"4\">Pixel-level</td></tr><tr><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUPRO</td></tr><tr><td>ViT-Small</td><td>37.4M</td><td>26.3G</td><td>153.6</td><td>99.26</td><td>99.67</td><td>98.72</td><td>98.07</td><td>68.29</td><td>67.78</td><td>94.36</td></tr><tr><td>ViT-Base†</td><td>148.0M</td><td>104.7G</td><td>58.1</td><td>99.60</td><td>99.78</td><td>99.04</td><td>98.35</td><td>69.29</td><td>69.17</td><td>94.79</td></tr><tr><td>ViT-Large</td><td>275.3M</td><td>413.5G</td><td>24.2</td><td>99.77</td><td>99.92</td><td>99.45</td><td>98.54</td><td>70.53</td><td>70.04</td><td>95.09</td></tr></table>",
+        "bbox": [
+            133,
+            128,
+            864,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/5f71ebbf272cad0fdc21a3279e913af6c14f1d181f64cbec2c34a88ad27b3447.jpg",
+        "table_caption": [
+            "Table 5. Scaling input size on MVTec-AD (\\%). †: default. Compared methods yield degradation when increasing input size."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Input Size</td><td>Image-Level</td><td>Pixel-Level</td></tr><tr><td rowspan=\"3\">RD4AD</td><td>2562†</td><td>94.6/96.5/96.1</td><td>96.1/48.6/53.8/91.1</td></tr><tr><td>3202</td><td>93.2/96.9/95.6</td><td>95.7/55.1/57.5/91.1</td></tr><tr><td>3842</td><td>91.9/96.2/95.0</td><td>94.9/52.1/55.3/90.8</td></tr><tr><td rowspan=\"3\">ReContrast</td><td>2562†</td><td>98.3/99.4/97.6</td><td>97.1/60.2/61.5/93.2</td></tr><tr><td>3202</td><td>98.2/99.2/97.5</td><td>96.8/61.8/62.6/93.3</td></tr><tr><td>3842</td><td>95.2/98.0/96.4</td><td>96.5/57.7/59.5/92.6</td></tr><tr><td rowspan=\"3\">Dinomaly</td><td>2802</td><td>99.6/99.8/99.3</td><td>98.2/65.2/66.3/93.6</td></tr><tr><td>3362</td><td>99.6/99.8/99.2</td><td>98.3/67.2/67.8/94.2</td></tr><tr><td>3922†</td><td>99.6/99.8/99.0</td><td>98.4/69.3/69.2/94.8</td></tr></table>",
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+        "type": "text",
+        "text": "Small has already produced state-of-the-art results. ViT-Large further boosts Dinomaly to an unprecedented higher record. This scalability enables users to choose an appropriate model size based on the computational resources available in their specific scenario. A comparison of computational costs with other methods is presented in Table A11. In addition, training schedule can also be scaled up for even better performance without increasing inference costs, as demonstrated in Figure 1 (Dinomaly $\\uparrow$ ).",
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+        "text": "Input Scalability. Though it seems unfair to compare Dinomaly with previous works that take smaller images as input, we contend that increasing their input size not only fails to benefit but actively undermines their performance, especially for image-level detection performance, as shown in Table 5. Therefore, we follow the common comparison strategy based on \"optimum vs. optimum\". On the contrary, Dinomaly enjoys scaling input size for anomaly localization, while still producing SoTA performance given smaller images. Details are presented in Table A2 in Appendix.",
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+        "text": "ViT Foundations. We conduct extensive experiments to investigate the impact of diverse pre-trained ViT foundations, including DeiT [50], MAE [19], D-iGPT [44], MOCOV3 [6], DINO [4], iBot [69], DINOv2 [39], and DINOv2-R [7]. As shown in Figure 5, Dinomaly is robust to the choice of backbone. Almost all foundation models can produce SoTA-level results with image-level AUROC higher than  $98\\%$ . The only notable exception is MAE, which, without fine-tuning, was reported to be less effective across various unsupervised tasks, e.g., kNN and linear-",
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+        "img_path": "images/7534438a9f00e66162f29b3e33941023cda6c2ee6fa9e8f5a27a44c64f62b210.jpg",
+        "image_caption": [
+            "Figure 5. Image-level AUROC of Dinomaly equipped with various ViT foundations, and their linear-probing accuracy on ImageNet. MIM: Masked Image Modeling. CL: Contrastive Learning."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "probing [39]. The optimal input size varies because the these backbones are pre-trained on different resolutions. Interestingly, we found the anomaly detection performance to be strongly correlated with the accuracy of ImageNet linear-probing (freeze backbone & only tune linear classifier) of the foundation model, suggesting the possibility of further improvement by simply adopting a future foundation model. Detailed results and analysis are presented in Appendix and Table A1.",
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+        "text": "Additional experiments and results are detailed in the Appendix C, encompassing evaluations of various pretrained foundations, ablation studies of each components, hyperparameter optimization, and other in-depth analyses.",
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+        "text": "5. Conclusion",
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+        "text": "Dinomaly, a minimalistic UAD framework, is proposed to address the under-performed MUAD models in this paper. We present four key elements in Dinomaly, i.e., Foundation Transformer, Noisy MLP Bottleneck, Linear Attention, and Loose Reconstruction, that can boost the performance under the challenging MUAD setting without fancy modules and tricks. Extensive experiments on MVTec AD, VisA, and Real-IAD demonstrate our superiority over previous model-unified multi-class models and even recent class-separated models, indicating the feasibility of implementing a unified model in complicated scenarios free of severe performance degradation.",
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+        "type": "text",
+        "text": "Acknowledgments",
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+        "type": "text",
+        "text": "References",
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2025/Dinomaly_ The Less Is More Philosophy in Multi-Class Unsupervised Anomaly Detection/269a00de-90dc-4a5c-8e52-737661810fb4_origin.pdf

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2025/Dinomaly_ The Less Is More Philosophy in Multi-Class Unsupervised Anomaly Detection/full.md

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+# Dinomaly: The Less Is More Philosophy in Multi-Class Unsupervised Anomaly Detection
+
+Jia Guo $^{1}$  Shuai Lu $^{2}$  Weihang Zhang $^{2\dagger}$  Fang Chen $^{3}$  Huiqi Li $^{2\dagger}$  Hongen Liao $^{1,3\boxtimes}$
+
+$^{1}$ School of Biomedical Engineering, Tsinghua University, Beijing, China  $^{2}$ Beijing Institute of Technology, Beijing, China
+
+$^{3}$ School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China
+
+guojia.jeremy@gmail.com lushuaie@163.com zhangweihang@bit.edu.cn chen-fang@sjtu.edu.cn huiqili@bit.edu.cn liao@tsinghua.edu.cn
+
+# Abstract
+
+Recent studies highlighted a practical setting of unsupervised anomaly detection (UAD) that builds a unified model for multi-class images. Despite various advancements addressing this challenging task, the detection performance under the multi-class setting still lags far behind state-of-the-art class-separated models. Our research aims to bridge this substantial performance gap. In this paper, we present Dinomaly, a minimalist reconstruction-based anomaly detection framework that harnesses pure Transformer architectures without relying on complex designs, additional modules, or specialized tricks. Given this powerful framework consisting of only Attentions and MLPs, we found four simple components that are essential to multi-class anomaly detection: (1) Scalable foundation Transformers that extracts universal and discriminative features, (2) Noisy Bottleneck where pre-existing Dropouts do all the noise injection tricks, (3) Linear Attention that naturally cannot focus, and (4) Loose Reconstruction that does not force layer-to-layer and point-by-point reconstruction. Extensive experiments are conducted across popular anomaly detection benchmarks including MVtec-AD, VisA, Real-IAD, etc. Our proposed Dinomaly achieves impressive image-level AUROC of  $99.6\%$ ,  $98.7\%$ , and  $89.3\%$  on the three datasets respectively, which is not only superior to state-of-the-art multi-class UAD methods, but also achieves the most advanced class-separated UAD records. Code is available at: https://github.com/guojiajeremy/Dinomaly
+
+# 1. Introduction
+
+Unsupervised anomaly detection (UAD) aims to detect abnormal patterns from normal images and further localize the anomalous regions. Because of the diversity of potential anomalies and their scarcity, this task is proposed to model the accessible training sets containing only normal samples as an unsupervised paradigm. UAD has a wide range of applications, e.g., industrial defect detection [3], medical disease screening [13], and video surveillance [37], addressing the difficulty of collecting and labeling all possible anomalies in these scenarios.
+
+Conventional works on UAD build a separate model for each object category, as shown in Figure 1(a). However, this one-class-one-model setting entails substantial storage overhead for saving models [60], especially when the application scenario necessitates a large number of object classes. For UAD methods, a compact boundary of normal patterns is vital to distinguish anomalies. Once the intra-normal patterns become exceedingly complicated due to various classes, the corresponding distribution becomes challenging to measure, consequently harming the detection performance. Recently, UniAD [60] and successive studies have been proposed to train a unified model for multi-class anomaly detection (MUAD), as shown in Figure 1(b). Under this setting, the "identity mapping" that directly copies the input as the output regardless of normal or anomaly harms the performance of conventional methods [60]. This phenomenon is caused by the diversity of multi-class normal patterns that drive the network to generalize on unseen patterns.
+
+Within two years, a number of methods have been proposed to address MUAD, such as neighbor-masked attention [60], synthetic anomalies [68], vector quantization [36], diffusion model [16, 59], and state space model (Mamba) [17]. However, there is still a non-negligible per
+
+![](images/e77de717e7226e870fe1250726262007dd1a4ff99ce23a99dd348328cf5b24f7.jpg)  
+(a) Class-Separated UAD Setting
+
+![](images/21af34168446ad566b0d66a8553a9bddb83a215a657a4e8c6b1775ed7512a181.jpg)  
+MVTec-AD (15 classes)
+
+![](images/752ff9fe62b375b33baafdeedcfd0b9ae29b5ad861e630b336cf9b22f9bea3ab.jpg)  
+VisA (12 classes)
+
+![](images/6de827691005c6a5c2758f19abd6cacf12119cbd3dd32c9c6d1fa1f13c2a2eae.jpg)  
+Real-IAD (30 classes)
+
+![](images/e357a9a888575f41ce9e2b5de7c3db2424bd3b9e759acf39d47a4e7ea73dcc37.jpg)  
+(b)  
+Model-Unified  
+Multi-Class UAD Setting
+
+![](images/bfa686fdd5f1898aaee9f58a6810b419098f70670743e14fdd62616ac3beeb8b.jpg)  
+(d) Scaling Properties of Dinomaly on MVTec-AD.  $\dagger$  : default setting.
+
+![](images/7c9079b35c2f53586e2ae811f1f5e9bee8e28950af1f243868cd1825e5748932.jpg)  
+(c) Image-Level AUROC on 3 Benchmarks
+
+![](images/3a384fc4fb010232dc6e2160c574502a492a9d1cb6613d52a8df42eb04d61f13.jpg)  
+Figure 1. Setting, benchmarking, and scaling of Dinomaly. (a) Task setting of class-separated UAD. (b) Task setting of MUAD. (c) Comparison with previous SoTA methods on MVtec-AD [3], VisA [70], and Real-IAD [54]. (d) Scaling properties of Dinomaly.
+
+formance gap between the state-of-the-art (SoTA) MUAD methods and class-separated UAD methods, restricting the practicability of implementing unified models, as shown in Figure 1(c). In addition, previous methods employ modules and architectures delicately designed, which may not be straightforward, and consequently suffer from limited universality and ease-of-use [18, 36].
+
+In this work, we aim to catch up with the performance of class-separated anomaly detection models using a multiclass unified model. We introduce Dinomaly, a minimalist reconstruction-based UAD framework built exclusively by pure Transformer blocks [51], specifically Self-Attentions and Multi-Layer Perceptrons (MLPs). To begin with, we empirically investigate the scaling law of self-supervised pre-trained Vision Transformers (ViT) [12] when serving as the feature encoders for extracting reconstruction objectives. Subsequently, we introduce three straightforward yet crucial elements to address the critical identity mapping phenomenon in MUAD contexts, without increasing complexity or computational burden. First, as an alternative to meticulously designed pseudo anomaly and feature noise, we propose to activate the built-in Dropout in an MLP to prevent the network from restoring both normal and anomalous patterns. Second, we propose to leverage the "side effect" of Linear Attention (a computation-efficient counterpart of Softmax Attention) that impedes focus on local regions, thus preventing the forwarding of identical information. Third, previous methods adopt layer-to-layer and region-by-region reconstruction schemes, distilling a decoder that can well mimic the encoder's behavior even for anomalous regions. Therefore, we propose to loosen the reconstruction constraints by grouping multiple layers as a
+
+whole and discarding well-reconstructed regions during optimization.
+
+To validate the effectiveness of the proposed Dinomaly under MUAD setting, we conduct extensive experiments on a number of widely used benchmarks, including MVTec AD [3] (15 classes), VisA [70] (12 classes), and RealIAD (30 classes). As shown in Figure 1, our base-size Dinomaly achieves unprecedented image-level AUROC of  $99.6\%$ ,  $98.7\%$ , and  $89.3\%$  on MVTec AD, VisA, and RealIAD, surpassing previous SoTA methods by a large margin. In addition, scalability is a key feature of Dinomaly. Further scaling up the model size maximizes performance to the fullest level of  $99.8\%$ ,  $98.9\%$ , and  $90.1\%$ , respectively; while scaling down parameters and input size can offer efficient solutions in computation-constrained scenarios.
+
+# 2. Related Work
+
+Multi-Class UAD. UniAD [60] first introduced multi-class anomaly detection, aiming to detect anomalies for different classes using a unified model. In this setting, conventional UAD methods often face the challenge of "identical shortcuts", where both anomaly-free and anomaly samples can be effectively recovered during inference [60]. It is believed that this phenomenon is caused by the diversity of multi-class normal patterns that drive the network to generalize on unseen patterns. This contradicts the fundamental assumption of epistemic methods. Many current researches focus on addressing this challenge [14, 31, 36, 59, 60]. UniAD [60] employs a neighbor-masked attention module and a feature-jitter strategy to mitigate these shortcuts. HVQ-Trans [36] proposes a vector quantization (VQ) Transformer model that induces large feature discrepancies
+
+![](images/17d3d0fa6c8cb95057e7196ca865d09815a7ac4253dda8c3a5682950e09bd3d4.jpg)  
+Figure 2. The framework of Dinomaly, built by simple and pure Transformer building blocks.
+
+for anomalies. LafitE [59] utilizes a latent diffusion model and introduces a feature editing strategy to alleviate this issue. DiAD [16] also employs diffusion models to address multi-class UAD settings. OmniAL [68] focuses on anomaly localization in the unified setting, preventing identical reconstruction by using synthesized pseudo anomalies. ReContrast [14] attempted to alleviate the identity mapping by cross-reconstruction between two encoders. ViTAD [5] abstracts a unified feature-reconstruction UAD framework and employ Transformer building blocks. MambaAD [17] explores the recently proposed State Space Model (SSM), Mamba, in the context of multi-class UAD. More related works of UAD are presented in Appendix A.
+
+# 3. Method
+
+# 3.1. Dinomaly Framework
+
+"What I cannot create, I do not understand"
+
+Richer Feynman
+
+The ability to recognize anomalies from what we know is an innate human capability, serving as a vital pathway for us to explore the world. Similarly, we construct a reconstruction-based framework that relies on the epistemic characteristic of artificial neural networks. Dinomaly consists of an encoder, a bottleneck, and a reconstruction decoder, as shown in Figure 2. Without loss of generality, a pretrained ViT network [12] with 12 Transformer layers is used as the encoder, extracting informative feature maps with different semantic scales. The bottleneck is a simple MLP (a.k.a. feed-forward network, FFN) that collects the feature representations of the encoder's 8 middle-level layers. The decoder is similar to the encoder, consisting of 8 Transformer layers. During training, the decoder learns to reconstruct the middle-level features of the encoder by maximizing the cosine similarity between feature maps. During inference, the decoder is expected to reconstruct normal regions of feature maps but fails for anomalous regions as it
+
+has never seen such samples.
+
+Foundation Transformers. Foundation models, especially ViTs [12, 33] pre-trained on large-scale datasets, serve as a basis and starting point for specific computer vision tasks. Such networks employ self-supervised learning schemes such as contrastive learning (MoCov3 [6], DINO [4]), masked image modeling (MAE [19], SimMIM [57], BEiT [40]), and their combination (iBOT [69], DINOv2 [39]), producing universal features suitable for image-level visual tasks and pixel-level visual tasks.
+
+Because of the lack of supervision in UAD, most advanced methods adopt pre-trained networks to extract discriminative features. Recent works [28, 43, 65] have preliminarily discovered the advantage of robust and universal features of self-supervised models over domain-specific ImageNet features in anomaly detection tasks. In this paper, we pioneer the investigation of scaling behaviors in UAD models through a systematic analysis of foundational ViTs, as briefed in Figure 1(d). Our comprehensive evaluation encompasses pre-training strategies (Figure 5), model sizes (Table 4), and input resolutions (Table 5), which are detailed in section 4.4. Considering the balance of detection performance and computational efficiency, we adopt ViT-Base/14 pretrained by DINoV2-Register [7] as the encoder of Dinomaly by default.
+
+# 3.2. Noisy Bottleneck.
+
+"Dropout is all you need."
+
+Prior studies [14, 60, 68] attribute the performance degradation of UAD methods trained on diverse multi-class samples to the "identity mapping" phenomenon; in this work, we reframe this issue as an "over-generalization" problem. Generalization ability is a merit of neural networks, allowing them to perform equally well on unseen test sets. However, generalization is not so wanted in the context of unsupervised anomaly detection that leverages the epistemic nature of neural networks. With the increas
+
+![](images/6d4a43b73593602e9e9d33bb1e07ed954c2eb370106d46e6efa33d5071ffbc4f.jpg)  
+Figure 3. Softmax Attention vs. Linear Attention. (a) Visualization of attention maps. (b) Attention distribution.
+
+![](images/8d125b0bc5327cd9d9792b71ec97f6b7783286bcb1c5a99b13be4c2f135ca734.jpg)
+
+ing diversity of images and their patterns due to multi-class UAD settings, the decoder can generalize its reconstruction ability to unseen anomalous samples, resulting in the failure of anomaly detection using reconstruction error.
+
+A direct solution for identity mapping is to shift "reconstruction" to "restoration". Specifically, instead of directly reconstructing the normal images or features given normal inputs, previous works propose to add perturbations as pseudo anomalies on input images [62, 67] or on encoder features [59, 60]; meanwhile, still let the decoder restore anomaly-free images or features, formulating a denoising-like framework. However, such methods employ heuristic and hand-crafted anomaly generation strategies that may not be universal across domains, datasets, and methods. In this work, we turn to leveraging the simple and elegant Dropout techniques. Since its introduction by Hinton et al. [21] in 2014 as a remedy for overfitting, Dropout has become a cornerstone element in neural architectures, including Transformers. In Dinomaly, we employ Dropout to randomly discard neural activations in an MLP bottleneck. Instead of alleviating overfitting, the role of Dropout in Dinomaly can be explained as pseudo feature anomaly that perturb normal representations, analogous to denoising auto-encoders [52, 53]. Without introducing any specific modules, this simple component inherently forces the decoder to restore normal features regardless of whether the test image contains anomalies, in turn, mitigating identical mapping.
+
+# 3.3. Unfocused Linear Attention.
+
+"One man's poison is another man's meat"
+
+Softmax Attention is the key mechanism of Transformers, allowing the model to attend to different parts of its
+
+input token sequence. Formally, given an input sequence  $\mathbf{X} \in \mathbb{R}^{N \times d}$  with length  $N$ , Attention first transforms it into three matrices: the query matrix  $\mathbf{Q} \in \mathbb{R}^{N \times d}$ , the key matrix  $\mathbf{K} \in \mathbb{R}^{N \times d}$ , and the value matrix  $\mathbf{V} \in \mathbb{R}^{N \times d}$ :
+
+$$
+\mathbf {Q} = \mathbf {X} \mathbf {W} ^ {Q}, \mathbf {K} = \mathbf {X} \mathbf {W} ^ {K}, \mathbf {V} = \mathbf {X} \mathbf {W} ^ {V}, \tag {1}
+$$
+
+where  $\mathbf{W}^Q, \mathbf{W}^K, \mathbf{W}^V \in \mathbb{R}^{d \times d}$  are learnable parameters. By computing the attention map by the query-key similarity, the output of Softmax Attention is given as:
+
+$$
+\operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {S o f t m a x} (\mathbf {Q K} ^ {T}) \mathbf {V}. \tag {2}
+$$
+
+Back to MUAD, previous methods [36, 60] suggest adopting Attentions instead of Convolutions because Convolutions can easily learn identical mappings. Nevertheless, both operations are in danger of forming identity mapping by over-concentrating on corresponding input locations for producing the outputs:
+
+$$
+\operatorname {C o n v} \operatorname {K e r n e l} = \left[ \begin{array}{l l l} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{array} \right], \quad \operatorname {A t t n} \operatorname {M a p} = \left[ \begin{array}{l l l} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right].
+$$
+
+Is there any simple solution that prevents Attentions from attending to identical information? In Dinomaly, we turn to leverage the "unfocusing ability" of a type of Softmax-free Attention, i.e., Linear Attention. Linear Attention was proposed as a promising alternative to reduce the computation complexity of vanilla Softmax Attention
+
+![](images/a1dd9fa401691a462a4df3a84a2f8feedcaf54499e447957f60fb2c121c62204.jpg)  
+(a) layer-to-layer sparse
+
+![](images/b866424b103ff548ef2ecbe121963fe58d37f24999027884bb87e659c5bc10ba.jpg)  
+(b) layer-to-cat-layer
+
+![](images/b4bffa389b2c5780fbe925887470053347f3965c3cfab98e72337e6b9155bdfe.jpg)  
+(c) layer-to-layer dense
+
+![](images/2e691d240b522deeace347316f62ed4982cc6efcf42bc8289ce3948972a78386.jpg)  
+(d) group-to-group 1 group (Ours)
+
+![](images/0302c001c32f5d638e646b4c5b0696ae395e2e4637f8de43dad4b5752f96a3ad.jpg)  
+(e) group-to-group 2 group (Ours)
+
+![](images/d3bc1adf7c570b9343648410728143a6c2329294536bf9af7d61d3b9329c354d.jpg)  
+encoder feature
+
+![](images/4767d4991e7ce4e01a71213986c2b2383e2a08849f258d4d882d31d17534b15e.jpg)  
+decoder feature
+
+![](images/f33596ba1387f7c0a6e5d9120039352aced6c9d016bf983caf8f1150221ea210.jpg)  
+reconstruct
+
+![](images/c37867f60176995bbf10bf74c757ea2ab30dd85d912f29e92525a9a0297ad90e.jpg)  
+concatenate
+
+![](images/ac76c81cae97fc845173fcf13a54643878bec7b040506ee9b893173e98d3134b.jpg)  
+add  
+Figure 4. Schemes of reconstruction constraint. (a) Layer-to-layer (sparse). (b) Layer-to-cat-layer. (c) Layer-to-layer (dense). (d) Loose group-to-group, 1-group (Ours). (e) Loose group-to-group, 2-group (Ours).
+
+concerning the number of tokens [26]. By substituting Softmax operation with a simple activation function  $\phi (\cdot)$  (usually  $\phi (x) = \mathrm{elu}(x) + 1$ ), we can change the computation order from  $(\mathbf{Q}\mathbf{K}^T)\mathbf{V}$  to  $\mathbf{Q}(\mathbf{K}^T\mathbf{V})$ . Formally, Linear Attention (LA) is given as:
+
+$$
+\operatorname {L A} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = (\phi (\mathbf {Q}) \phi \left(\mathbf {K} ^ {T}\right)) \mathbf {V} = \phi (\mathbf {Q}) \left(\phi \left(\mathbf {K} ^ {T}\right) \mathbf {V}\right), \tag {3}
+$$
+
+where the computation complexity is reduced to  $\mathcal{O}(Nd^2)$  from  $\mathcal{O}(N^2 d)$ . The trade-off between complexity and expressiveness is a dilemma. Previous studies [15, 48] attribute Linear Attention's performance degradation on supervised tasks to its incompetence in focusing. Due to the absence of non-linear attention reweighting by Softmax operation, Linear Attention cannot concentrate on important regions related to the query, such as foreground and neighbors. This property, however, is exactly what the reconstruction decoder favors in our contexts.
+
+In order to probe how Attentions propagate information, we train two variants of Dinomaly using vanilla Softmax Attention or Linear Attention as the spatial mixer in the decoder and visualize their attention maps. As shown in Figure 3, Softmax Attention tends to focus on the exact region of the query, while Linear Attention spreads its attention across the whole image. This implies that Linear Attention, forced by its incompetence to focus, utilizes more long-range information to restore features at each position, reducing the chance of passing identical information of unseen patterns to the next layer during reconstruction. Of course, employing Linear Attention also benefits from less computation, free of performance drop.
+
+# 3.4. Loose Reconstruction
+
+"The tighter you squeeze, the less you have."
+
+Loose Constraint. Pioneers of feature-reconstruction/distillation UAD methods [10, 46] are inspired by knowledge distillation [20]. Most reconstruction-based methods distill specific encoder layers (e.g. 3 last layers of 3 ResNet stages) by the corresponding decoder layers [10, 46, 65] (Figure 4(a)) or the last decoder layer [58, 60] (Figure 4(b)). Intuitively, with more encoder-decoder feature pairs (Figure 4(c)), UAD model can utilize
+
+more information in different layers to discriminate anomalies. However, according to the intuition of knowledge distillation, the student (decoder) can better mimic the behavior of the teacher (encoder) given more layer-to-layer supervision [30], which is harmful for UAD models that detect anomalies by encoder-decoder discrepancy. This phenomenon is also embodied as identity mapping. Thanks to the top-to-bottom consistency of columnar Transformer layers, we propose to loosen the layer-to-layer constraint by adding up all feature maps of interested layers as a whole group, as shown in Figure 4(d). This scheme can be seen as loosening the layer-to-layer correspondence and providing the decoder with more degrees of freedom, so that the decoder is allowed to act much more differently from the encoder when the input pattern is unseen. Because features of shallow layers contain low-level visual characters that are helpful for precise localization, we can further group the features into the low-semantic-level group and high-semantic-level group, as shown in Figure 4(e).
+
+**Loose Loss.** Following the above analysis, we also loosen the point-by-point reconstruction loss function by discarding some points in the feature map. Here, we simply borrow the hard-mining global cosine loss [14] that detaches the gradients of well-restored feature points with low cosine distance during training. Let  $f_{E}$  and  $f_{D}$  denotes (grouped) feature maps of encoder and decoder:
+
+$$
+\mathcal {L} _ {\text {g l o b a l} - h m} = \mathcal {D} _ {\text {c o s}} \left(\mathcal {F} \left(f _ {E}\right), \mathcal {F} \left(\hat {f} _ {D}\right)\right), \tag {4}
+$$
+
+$$
+\hat {f} _ {D} (h, w) = \left\{ \begin{array}{l} s g \left(f _ {D} (h, w)\right)_{0.1}, \text {if} \mathcal {D} _ {\text {cos}} \left(f _ {D}, f _ {E}\right) <   k \% _ {\text {batch}} \\ f _ {D} (h, w), \text {else} \end{array} \right. \tag{5}
+$$
+
+$$
+\mathcal {D} _ {\cos} (a, b) = 1 - \frac {a ^ {T} \cdot b}{\| a \| \| b \|}, \tag {6}
+$$
+
+where  $\mathcal{D}_{cos}$  denotes cosine distance,  $\mathcal{F}(\cdot)$  denotes flatten operation,  $f_{D}(h,w)$  represents the feature point at  $(h,w)$ , and  $sg(\cdot)_{0.1}$  denotes shrink the gradient to one-tenth of the original  $^2$ .  $\mathcal{D}_{cos}(f_D(h,w),f_E(h,w)) < k\%_{batch}$  selects  $k \%$  feature points with smaller cosine distance within a batch for gradient shrinking. Total loss is the average  $\mathcal{L}_{global - hm}$  of all encoder-decoder feature pairs.
+
+Table 1. Performance under multi-class UAD setting (%). †: method designed for MUAD. Dinomaly†: training schedule is scaled up to 20,000, 20,000, and 100,000 iterations (original: 10,000/10,000/50,000).  
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Method</td><td colspan="3">Image-level</td><td colspan="4">Pixel-level</td></tr><tr><td>AUROC</td><td>AP</td><td>\(F_1\)-max</td><td>AUROC</td><td>AP</td><td>\(F_1\)-max</td><td>AUPRO</td></tr><tr><td rowspan="10">MVTec-AD [3]</td><td>RD4AD [10]</td><td>94.6</td><td>96.5</td><td>95.2</td><td>96.1</td><td>48.6</td><td>53.8</td><td>91.1</td></tr><tr><td>SimpleNet [34]</td><td>95.3</td><td>98.4</td><td>95.8</td><td>96.9</td><td>45.9</td><td>49.7</td><td>86.5</td></tr><tr><td>DeSTSeg [67]</td><td>89.2</td><td>95.5</td><td>91.6</td><td>93.1</td><td>54.3</td><td>50.9</td><td>64.8</td></tr><tr><td>UniAD [60]†</td><td>96.5</td><td>98.8</td><td>96.2</td><td>96.8</td><td>43.4</td><td>49.5</td><td>90.7</td></tr><tr><td>ReContrast [14]†</td><td>98.3</td><td>99.4</td><td>97.6</td><td>97.1</td><td>60.2</td><td>61.5</td><td>93.2</td></tr><tr><td>DiAD [18]†</td><td>97.2</td><td>99.0</td><td>96.5</td><td>96.8</td><td>52.6</td><td>55.5</td><td>90.7</td></tr><tr><td>ViTAD [65]†</td><td>98.3</td><td>99.4</td><td>97.3</td><td>97.7</td><td>55.3</td><td>58.7</td><td>91.4</td></tr><tr><td>MambaAD [17]†</td><td>98.6</td><td>99.6</td><td>97.8</td><td>97.7</td><td>56.3</td><td>59.2</td><td>93.1</td></tr><tr><td>Dinomaly (Ours)</td><td>99.6</td><td>99.8</td><td>99.0</td><td>98.4</td><td>69.3</td><td>69.2</td><td>94.8</td></tr><tr><td>Dinomaly†</td><td>99.7</td><td>99.8</td><td>99.2</td><td>98.4</td><td>69.3</td><td>69.2</td><td>94.7</td></tr><tr><td rowspan="10">VisA [70]</td><td>RD4AD [10]</td><td>92.4</td><td>92.4</td><td>89.6</td><td>98.1</td><td>38.0</td><td>42.6</td><td>91.8</td></tr><tr><td>SimpleNet [34]</td><td>87.2</td><td>87.0</td><td>81.8</td><td>96.8</td><td>34.7</td><td>37.8</td><td>81.4</td></tr><tr><td>DeSTSeg [67]</td><td>88.9</td><td>89.0</td><td>85.2</td><td>96.1</td><td>39.6</td><td>43.4</td><td>67.4</td></tr><tr><td>UniAD [60]†</td><td>88.8</td><td>90.8</td><td>85.8</td><td>98.3</td><td>33.7</td><td>39.0</td><td>85.5</td></tr><tr><td>ReContrast [14]†</td><td>95.5</td><td>96.4</td><td>92.0</td><td>98.5</td><td>47.9</td><td>50.6</td><td>91.9</td></tr><tr><td>DiAD [18]†</td><td>86.8</td><td>88.3</td><td>85.1</td><td>96.0</td><td>26.1</td><td>33.0</td><td>75.2</td></tr><tr><td>ViTAD [65]†</td><td>90.5</td><td>91.7</td><td>86.3</td><td>98.2</td><td>36.6</td><td>41.1</td><td>85.1</td></tr><tr><td>MambaAD [17]†</td><td>94.3</td><td>94.5</td><td>89.4</td><td>98.5</td><td>39.4</td><td>44.0</td><td>91.0</td></tr><tr><td>Dinomaly (Ours)</td><td>98.7</td><td>98.9</td><td>96.2</td><td>98.7</td><td>53.2</td><td>55.7</td><td>94.5</td></tr><tr><td>Dinomaly†</td><td>98.9</td><td>99.0</td><td>96.4</td><td>98.8</td><td>53.8</td><td>55.8</td><td>94.5</td></tr><tr><td rowspan="10">Real-IAD [54]</td><td>RD4AD [10]</td><td>82.4</td><td>79.0</td><td>73.9</td><td>97.3</td><td>25.0</td><td>32.7</td><td>89.6</td></tr><tr><td>SimpleNet [34]</td><td>57.2</td><td>53.4</td><td>61.5</td><td>75.7</td><td>2.8</td><td>6.5</td><td>39.0</td></tr><tr><td>DeSTSeg [67]</td><td>82.3</td><td>79.2</td><td>73.2</td><td>94.6</td><td>37.9</td><td>41.7</td><td>40.6</td></tr><tr><td>UniAD [60]†</td><td>83.0</td><td>80.9</td><td>74.3</td><td>97.3</td><td>21.1</td><td>29.2</td><td>86.7</td></tr><tr><td>ReContrast [14]†</td><td>86.4</td><td>84.2</td><td>77.4</td><td>97.8</td><td>31.6</td><td>38.2</td><td>91.8</td></tr><tr><td>DiAD [18]†</td><td>75.6</td><td>66.4</td><td>69.9</td><td>88.0</td><td>2.9</td><td>7.1</td><td>58.1</td></tr><tr><td>ViTAD [65]†</td><td>82.7</td><td>80.2</td><td>73.7</td><td>97.2</td><td>24.3</td><td>32.3</td><td>84.8</td></tr><tr><td>MambaAD [17]†</td><td>86.3</td><td>84.6</td><td>77.0</td><td>98.5</td><td>33.0</td><td>38.7</td><td>90.5</td></tr><tr><td>Dinomaly (Ours)</td><td>89.3</td><td>86.8</td><td>80.2</td><td>98.8</td><td>42.8</td><td>47.1</td><td>93.9</td></tr><tr><td>Dinomaly†</td><td>89.5</td><td>86.9</td><td>80.4</td><td>98.9</td><td>43.3</td><td>47.4</td><td>94.2</td></tr></table>
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Datasets. MVtec-AD [3] contains 15 objects (5 texture classes and 10 object classes) with a total of 3,629 normal images as the training set and 1,725 images as the test set (467 normal, 1,258 anomalous). VisA [70] contains 12 objects. Training and test sets are split following the official splitting, resulting in 8,659 normal images in the training set and 2,162 images in the test set (962 normal, 1,200 anomalous). Real-IAD [54] is a large UAD dataset recently released, containing 30 distinct objects. We follow the official splitting that includes all views, resulting in 36,465 normal images in the training set and 114,585 images in the test set (63,256 normal, 51,329 anomalous).
+
+Metrics. Following prior works [17, 65], we adopt 7 evaluation metrics. Image-level anomaly detection performance is measured by the Area Under the Receiver Operator Curve (AUROC), Average Precision (AP), and  $F_{1}$  score under optimal threshold  $(F_{1}$ -max). Pixel-level anomaly localization is measured by AUROC, AP,  $F_{1}$ -max and the Area Under the Per-Region-Overlap (AUPRO). The results
+
+of a dataset is the average of all classes.
+
+Implementation Details. ViT-Base/14 (patchsize=14) pre-trained by DINOv2-R [7] is used as the encoder by default. The drop rate of Noisy Bottleneck is 0.2 by default and increases to 0.4 on the diverse Real-IAD. Loose constraint with 2 groups is employed, and the anomaly map is given by the mean per-point cosine distance of the 2 groups. The input image is first resized to  $448^2$  and then center-cropped to  $392^2$ , so the feature map  $(28^2)$  is large enough for anomaly localization. StableAdamW optimizer [56] with AMSGrad [41] (more stable than AdamW [35] in training) is utilized with  $lr = 2e - 3$ ,  $\beta = (0.9,0.999)$  and  $wd = 1e - 4$ . The network is trained for 10,000 iterations (steps) on MVTec-AD and VisA, and 50,000 iterations on Real-IAD. Detailed settings are available in Appendix B.
+
+# 4.2. Comparison to Multi-Class UAD SoTAs
+
+We compare the proposed Dinomaly with the most advanced UAD and MUAD methods [10, 14, 17, 18, 34, 65, 67]. Experimental results are presented in Table 1, where Dinomaly surpasses compared methods by a large margin on all datasets and all metrics. On the most
+
+Table 2. Performance under conventional class-separated UAD setting (%). n/a: not available.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">MVTec-AD [3]</td><td colspan="3">VisA [70]</td><td colspan="3">Real-IAD [54]</td></tr><tr><td>I-AUROC</td><td>P-AUROC</td><td>P-AUPRO</td><td>I-AUROC</td><td>P-AUROC</td><td>P-AUPRO</td><td>I-AUROC</td><td>P-AUROC</td><td>P-AUPRO</td></tr><tr><td>Dinomaly (MUAD)</td><td>99.6</td><td>98.4</td><td>94.8</td><td>98.7</td><td>98.7</td><td>94.5</td><td>89.3</td><td>98.8</td><td>93.9</td></tr><tr><td>Dinomaly</td><td>99.7</td><td>99.9</td><td>95.0</td><td>98.9</td><td>98.9</td><td>95.1</td><td>92.0</td><td>99.1</td><td>95.1</td></tr><tr><td>RD4AD [10]</td><td>98.5</td><td>97.8</td><td>93.9</td><td>96.0</td><td>90.1</td><td>70.9</td><td>87.1</td><td>n/a</td><td>93.8</td></tr><tr><td>PatchCore [45]</td><td>99.1</td><td>98.1</td><td>93.5</td><td>94.7</td><td>98.5</td><td>91.8</td><td>89.4</td><td>n/a</td><td>91.5</td></tr><tr><td>SimpleNet [34]</td><td>99.6</td><td>98.1</td><td>90.0</td><td>97.1</td><td>98.2</td><td>90.7</td><td>88.5</td><td>n/a</td><td>84.6</td></tr></table>
+
+Table 3. Ablations of Dinomaly elements on MVTec-AD (%). NB: Noisy Bottleneck. LA: Linear Attention. LC: Loose Constraint (2 groups). LL: Loose Loss. As MVTec-AD has reached saturation, we also present the results on VisA (Table A4).  
+
+<table><tr><td rowspan="2">NB</td><td rowspan="2">LA</td><td rowspan="2">LC</td><td rowspan="2">LL</td><td colspan="3">Image-level</td><td colspan="4">Pixel-level</td></tr><tr><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUPRO</td></tr><tr><td></td><td></td><td></td><td></td><td>98.41</td><td>99.09</td><td>97.41</td><td>97.18</td><td>62.96</td><td>63.82</td><td>92.95</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>99.06</td><td>99.54</td><td>98.31</td><td>97.62</td><td>66.22</td><td>66.70</td><td>93.71</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>98.54</td><td>99.21</td><td>97.62</td><td>97.20</td><td>62.94</td><td>63.73</td><td>93.09</td></tr><tr><td></td><td></td><td>✓</td><td></td><td>98.35</td><td>99.04</td><td>97.43</td><td>97.10</td><td>61.05</td><td>62.73</td><td>92.60</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>99.03</td><td>99.45</td><td>98.19</td><td>97.62</td><td>64.10</td><td>64.96</td><td>93.34</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>99.27</td><td>99.62</td><td>98.63</td><td>97.85</td><td>67.36</td><td>67.33</td><td>94.16</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>99.50</td><td>99.72</td><td>98.87</td><td>98.14</td><td>68.16</td><td>68.24</td><td>94.23</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>99.52</td><td>99.73</td><td>98.92</td><td>98.20</td><td>68.25</td><td>68.34</td><td>94.17</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>99.57</td><td>99.78</td><td>99.00</td><td>98.20</td><td>67.93</td><td>68.21</td><td>94.50</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>99.60</td><td>99.78</td><td>99.04</td><td>98.35</td><td>69.29</td><td>69.17</td><td>94.79</td></tr></table>
+
+widely used MVTec-AD, Dinomaly produces image-level performance of 99.6/99.8/99.0 (\%) and pixel-level performance of 98.4/69.3/69.2/94.8, outperforming previous SoTAs by 1.0/0.2/1.2 and 0.7/9.1/7.7/1.6. This result declares that the image-level performance on the MVTec-AD dataset is nearly saturated under the MUAD setting. On the popular VisA, Dinomaly achieves image-level performance of 98.7/98.9/96.2 and pixel-level performance of 98.7/53.2/55.7/94.5, outperforming previous SoTAs by 3.2/2.5/4.2 and 0.2/5.3/5.1/2.6. On the Real-IAD that contains 30 classes, each with 5 camera views, we produce image-level and pixel-level performance of 89.3/86.8/80.2 and 98.8/42.8/47.1/93.9, outperforming previous SoTAs by 3.0/2.2/3.2 and 0.3/4.9/5.4/3.4, indicating our scalability to extremely complex scenarios. Per-class performances and qualitative visualization are presented in Appendix E and F. We also produce superior results on other popular UAD benchmarks, i.e., MPDD [24], BTAD [38], and UniMedical [66], with I-AUROC of 97.2, 95.4, and 84.9, respectively, as shown in Table A13 in Appendix.
+
+# 4.3. Comparison to Class-Separated UAD SoTAs
+
+Dinomaly is also compared with class-separated SoTAs, as shown in Table 2. Dinomaly under MUAD setting is comparable to conventional methods [10, 34, 45] that build individual models for each class. On MVTec-AD and VisA, multi-class Dinomaly (first row) is subjected to nearly no
+
+performance drop compared to its class-separated counterpart (second row). On the complicated Real-IAD that involves more classes and views, multi-class Dinomaly suffers a moderate performance drop but is still comparable to class-separated SoTAs.
+
+# 4.4. Ablation Study
+
+Overall Ablation. We conduct experiments to verify the effectiveness of the proposed elements, i.e., Noisy Bottleneck (NB), Linear Attention (LA), Loose Constraint (LC), and Loose Loss (LL). The already-powerful baseline (first row) is Dinomaly with noiseless MLP bottleneck, Softmax Attention, dense layer-to-layer supervision, and global cosine loss. This baseline is very similar to ViTAD [64] and the ViT version of RD4AD [10]. Results on MVtec-AD and VisA are shown in Table 3 and Table A4, respectively. NB and LL can directly contribute to the model performance. LA and LC boost the performance with the presence of NB. The use of LC is not solely beneficial because LC makes the reconstruction too easy without injected noise.
+
+Model Scalability. Previous works [10, 60, 65] reported that anomaly detection networks do not follow the "scaling law". For example, RD4AD [10] found WideResNet50 better than WideResNet101 as the encoder backbone. ViTAD [65] found ViT-Small better than ViT-Base. On the contrary, as shown in Table 4, the performance of the proposed Dinomaly benefits from scaling. Dinomaly equipped with ViT
+
+Table 4. Scaling of ViT model sizes on MVtec-AD (%). Im/s (Throughoutput, image per second) is measured on NVIDIA RTX3090 with batch size=16. Results on VisA and Real-IAD are shown in Table A3. †:default.  
+
+<table><tr><td rowspan="2">Arch.</td><td rowspan="2">Params</td><td rowspan="2">MACs</td><td rowspan="2">Im/s</td><td colspan="3">Image-level</td><td colspan="4">Pixel-level</td></tr><tr><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUROC</td><td>AP</td><td>F1-max</td><td>AUPRO</td></tr><tr><td>ViT-Small</td><td>37.4M</td><td>26.3G</td><td>153.6</td><td>99.26</td><td>99.67</td><td>98.72</td><td>98.07</td><td>68.29</td><td>67.78</td><td>94.36</td></tr><tr><td>ViT-Base†</td><td>148.0M</td><td>104.7G</td><td>58.1</td><td>99.60</td><td>99.78</td><td>99.04</td><td>98.35</td><td>69.29</td><td>69.17</td><td>94.79</td></tr><tr><td>ViT-Large</td><td>275.3M</td><td>413.5G</td><td>24.2</td><td>99.77</td><td>99.92</td><td>99.45</td><td>98.54</td><td>70.53</td><td>70.04</td><td>95.09</td></tr></table>
+
+Table 5. Scaling input size on MVTec-AD (\%). †: default. Compared methods yield degradation when increasing input size.  
+
+<table><tr><td>Method</td><td>Input Size</td><td>Image-Level</td><td>Pixel-Level</td></tr><tr><td rowspan="3">RD4AD</td><td>2562†</td><td>94.6/96.5/96.1</td><td>96.1/48.6/53.8/91.1</td></tr><tr><td>3202</td><td>93.2/96.9/95.6</td><td>95.7/55.1/57.5/91.1</td></tr><tr><td>3842</td><td>91.9/96.2/95.0</td><td>94.9/52.1/55.3/90.8</td></tr><tr><td rowspan="3">ReContrast</td><td>2562†</td><td>98.3/99.4/97.6</td><td>97.1/60.2/61.5/93.2</td></tr><tr><td>3202</td><td>98.2/99.2/97.5</td><td>96.8/61.8/62.6/93.3</td></tr><tr><td>3842</td><td>95.2/98.0/96.4</td><td>96.5/57.7/59.5/92.6</td></tr><tr><td rowspan="3">Dinomaly</td><td>2802</td><td>99.6/99.8/99.3</td><td>98.2/65.2/66.3/93.6</td></tr><tr><td>3362</td><td>99.6/99.8/99.2</td><td>98.3/67.2/67.8/94.2</td></tr><tr><td>3922†</td><td>99.6/99.8/99.0</td><td>98.4/69.3/69.2/94.8</td></tr></table>
+
+Small has already produced state-of-the-art results. ViT-Large further boosts Dinomaly to an unprecedented higher record. This scalability enables users to choose an appropriate model size based on the computational resources available in their specific scenario. A comparison of computational costs with other methods is presented in Table A11. In addition, training schedule can also be scaled up for even better performance without increasing inference costs, as demonstrated in Figure 1 (Dinomaly $\uparrow$ ).
+
+Input Scalability. Though it seems unfair to compare Dinomaly with previous works that take smaller images as input, we contend that increasing their input size not only fails to benefit but actively undermines their performance, especially for image-level detection performance, as shown in Table 5. Therefore, we follow the common comparison strategy based on "optimum vs. optimum". On the contrary, Dinomaly enjoys scaling input size for anomaly localization, while still producing SoTA performance given smaller images. Details are presented in Table A2 in Appendix.
+
+ViT Foundations. We conduct extensive experiments to investigate the impact of diverse pre-trained ViT foundations, including DeiT [50], MAE [19], D-iGPT [44], MOCOV3 [6], DINO [4], iBot [69], DINOv2 [39], and DINOv2-R [7]. As shown in Figure 5, Dinomaly is robust to the choice of backbone. Almost all foundation models can produce SoTA-level results with image-level AUROC higher than  $98\%$ . The only notable exception is MAE, which, without fine-tuning, was reported to be less effective across various unsupervised tasks, e.g., kNN and linear-
+
+![](images/7534438a9f00e66162f29b3e33941023cda6c2ee6fa9e8f5a27a44c64f62b210.jpg)  
+Figure 5. Image-level AUROC of Dinomaly equipped with various ViT foundations, and their linear-probing accuracy on ImageNet. MIM: Masked Image Modeling. CL: Contrastive Learning.
+
+probing [39]. The optimal input size varies because the these backbones are pre-trained on different resolutions. Interestingly, we found the anomaly detection performance to be strongly correlated with the accuracy of ImageNet linear-probing (freeze backbone & only tune linear classifier) of the foundation model, suggesting the possibility of further improvement by simply adopting a future foundation model. Detailed results and analysis are presented in Appendix and Table A1.
+
+Additional experiments and results are detailed in the Appendix C, encompassing evaluations of various pretrained foundations, ablation studies of each components, hyperparameter optimization, and other in-depth analyses.
+
+# 5. Conclusion
+
+Dinomaly, a minimalistic UAD framework, is proposed to address the under-performed MUAD models in this paper. We present four key elements in Dinomaly, i.e., Foundation Transformer, Noisy MLP Bottleneck, Linear Attention, and Loose Reconstruction, that can boost the performance under the challenging MUAD setting without fancy modules and tricks. Extensive experiments on MVTec AD, VisA, and Real-IAD demonstrate our superiority over previous model-unified multi-class models and even recent class-separated models, indicating the feasibility of implementing a unified model in complicated scenarios free of severe performance degradation.
+
+# Acknowledgments
+
+# References
+
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+[11] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In IEEE Conference on Computer Vision and Pattern Recognition, pages 248–255, 2009. 2
+
+The authors acknowledge supports from National Natural Science Foundation of China (U22A2051, 82027807), National Key Research and Development Program of China (2022YFC2405200), Tsinghua-Foshan Innovation Special Fund (2021THFS0104), and Institute for Intelligent Healthcare, Tsinghua University (2022ZLB001).  
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+        "type": "text",
+        "text": "DirectTriGS: Triplane-based Gaussian Splitting Field Representation for 3D Generation",
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+        "text": "Xiaoliang Ju, Hongsheng Li $^{1,2}$ $^{1}$  CUHK MMLab  $^{2}$  CPII under InnoHK",
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+        "text": "akira@link.cuhk.edu.hk",
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+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We present DirectTriGS, a novel framework designed for 3D object generation with Gaussian Splatting (GS). GS-based rendering for 3D content has gained considerable attention recently. However, there has been limited exploration in directly generating 3D Gaussians compared to traditional generative modeling approaches. The main challenge lies in the complex data structure of GS represented by discrete point clouds with multiple channels. To overcome this challenge, we propose employing the triplane representation, which allows us to represent Gaussian Splatting as an image-like continuous field. This representation effectively encodes both the geometry and texture information, enabling smooth transformation back to Gaussian point clouds and rendering into images by a TriRenderer, with only 2D supervisions. The proposed TriRenderer is fully differentiable, so that the rendering loss can supervise both texture and geometry encoding. Furthermore, the triplane representation can be compressed using a Variational Autoencoder (VAE), which can subsequently be utilized in latent diffusion to generate 3D objects. The experiments demonstrate that the proposed generation framework can produce high-quality 3D object geometry and rendering results in the text-to-3D task.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
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+    },
+    {
+        "type": "text",
+        "text": "Neural rendering has grown to a focal point in rendering techniques in recent years, as it achieves more realistic rendering effects by leveraging the great expressiveness of neural network. The representatives are neural radiance field (NeRF) [32] and the newly emerged Gaussian Splatting (GS) [21]. However, when applied to the field of 3D generation, the slow rendering and training speed become a strong limitation for NeRF. While GS is more flexible with greater rendering efficiency and editability, few works have addressed the challenge of direct GS generation in 3D due to its complex data structure. In this paper, we propose a",
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "novel approach called DirectTriGS, which encodes GS as triplane representation, and introduce its corresponding renderer, TriRenderer. Subsequently, we apply latent diffusion on the Triplane representation to generate high-quality GS objects.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Gaussian splatting uses multi-channel point cloud of \"splats\" to describe the 3D contents. With a differentiable splats rasterizer, GS has fast rendering speed. However, the sparsity, multiple channels, and uneven distributed density of 3D GS bring great difficulty for 3D generation. We propose to encode GS contents as multi-channel triplane representations, which have been shown to possess favorable properties for representing 3D geometry or NeRF, as demonstrated in previous works Shue et al. [40], Wu et al. [47]. In our work, we leverage the triplane representation to encode both the geometry information and other GS attributes in two separate groups of channels. By training on a dataset of 3D objects, we obtain a shared TriRenderer that is capable of decoding different triplane representations to GS and then render it to image. TriRenderer is fully differentiable, enabling the use of only 2D rendering loss to supervise both the texture and geometry of 3D GS. The advantage of using Triplane to represent GS are two folds. First, it leads to high memory efficiency compared with dense voxels and is expressive enough for generating various 3D GS. Second, Triplane is more compatible with the convolution-based encoders compared with the original sparse GS point cloud, which require specifically designed networks on processing sparse point clouds.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We follow stable diffusion [36] to train DirectTriGS on the proposed triplane representation. Specifically, a VAE is designed to further convert the Triplanes into latent code. We use two separate decoders to decouple the decoding of geometry and GS attributes. Second, we roll out the triplane latent to an expanded multi-channel image, then exploit staged latent diffusion to do generation. Two-stage diffusion is employed to generate the geometry and the corresponding GS appearance. Finally, score distillation sampling (SDS) [35] is adopted as a optional post-processing to refine or restyle the generated 3D objects.",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "16229",
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+    {
+        "type": "text",
+        "text": "Our contribution can summarize as follows. 1) We propose a Triplane representation for direct 3D GS generation, which is memory efficient to derive GS point clouds with vivid rendering. 2) We design a fully differentiable TriRenderer to enable the end-to-end training of triplane representations, with only 2D supervisions. 3) We develop a Triplane-based GS generation framework DirectTriGS that incorporates a specially designed VAE, latent diffusion module, and a SDS based refiner. 4) Experiments demonstrate our method produces competitive performance in both 3D geometry and multi-view rendering quality in text-to-3D tasks.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3D Object Generation. 1) Multi-view images-to-3D. The first route generates multi-view colored 3D image and then reconstruct the 3D shape and project image to texture, or use score distillation sampling to build 3D object from images produced by 2D diffusion, such as [6, 13, 27, 35, 39, 41]. Since these approaches are actually 2D generator, it is difficult to maintain 3D consistency, which may lead to Janus problem. 2) Image-to-3D. The second route attempt to retrieve 3D geometry from a single input image, such as [25, 28, 53]. With the certain one image as input, the users may be more concerned with the reconstruction quality. 3)Text-to-3D. The third group mainly operate in 3D, which can be clustered by different 3D representation. For example, [10, 11] are able to generate high-quality 3D textured meshes using differentiable rendering; [34, 46] generate colored pointcloud; [1, 14, 23, 31] generate NeRF volumes; [18, 47] generate SDF volumes.",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Remark. The input conditions of these three generation methods are gradually becoming abstract, corresponding to increasing difficulty of the generation task, commonly resulting in a gradual decline in the generation quality.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Gaussian Splatting. Gaussian Splatting [21] exploits multi-channel pointcloud of splats to describe the 3D content, which allows real-time rendering of photorealistic scenes. Recently, there emerges so many research focusing on its reconstruction quality enhancement and algorithm optimization [5, 8, 15, 29, 51]. Another related active area includes 4D dynamic GS modeling [3, 44, 49], scene editing [2, 9] and its applications like SLAM [30, 48].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As for GS generation, some works exploit multi-view image based route such as [6, 41], where the image generator output image from required views to enhance the GS rendering in a recursive manner. Rare works explore the GS generation directly in 3D space, such as [53] generates a point cloud using a Transformer structure with 2D image as input, and build a mapping of image to tri-plane encoding of GS attribute; GaussianCube [52] proposes to use optimal transport to model the 3D GS for text-to-3D generation; [16] combine explicit anchor points with implicit",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "triplane to directly generate GS points.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Revisiting Gaussian Splitting",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Gaussian Splatting [21] uses a set of Gaussian points to describe a 3D object. The Gaussian points are defined by a full 3D covariance matrix  $\\pmb{\\Sigma}$  in a world space as  $G(\\mathbf{x}) = e^{-\\frac{1}{2}\\mathbf{x}^T\\pmb{\\Sigma}^{-1}\\mathbf{x}}$ , centered at point (mean)  $\\mathbf{p} \\in \\mathbb{R}^3$ . Each point is with a opacity scalar  $\\alpha \\in [0,1]$  for blending and a series of Spherical Harmonics (SH) coefficients to correctly capture the view-dependent appearance of the scene. The number of SH coefficients are  $3 \\times (n + 1)^2$ , where  $n$  denotes the SH order, and higher  $n$  corresponds to more accurate view-dependent appearance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "During rendering, the Gaussians are project to 2D given a viewing transformation  $\\mathbf{W}$ . The covariance is transformed as  $\\boldsymbol{\\Sigma}^{\\prime} = \\mathbf{J}\\mathbf{W}\\boldsymbol{\\Sigma}\\mathbf{W}^{T}\\mathbf{J}^{T}$ , where  $\\mathbf{J}$  is the Jacobian of the affine approximation of the projective transformation. To ensure  $\\boldsymbol{\\Sigma}$  to be semi-positive in the whole training process,  $\\boldsymbol{\\Sigma}$  can be represented by a Cholesky decomposition as  $\\boldsymbol{\\Sigma} = \\mathbf{R}\\mathbf{S}\\mathbf{S}^{T}\\mathbf{R}^{T}$ , represented by a tuple  $s = (s_{1}, s_{2}, s_{3})$  for scaling and a unnormalized quaternion  $\\mathbf{q} \\in \\mathbb{R}^{4}$  for rotation. In summary, each Gaussian point are a union set of position  $\\mathbf{p}$  and its GS attributes:",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {G} _ {\\mathbf {p}} := \\{s, \\mathbf {q}, \\mathrm {S H}, \\alpha \\}. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "GS pointcloud can be efficiently rendered by a rasterization-based splatting renderer [21], which is fully differentiable.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4. Methodology",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Our motivation is to directly generate 3D GS with fast speed by utilizing the proposed triplane-based GS representation. While 2D-lifting methods like SDS-based approaches yield intricate results, they are time-intensive and susceptible to Janus problem. Direct generation, notably with fast sampling, can complete 3D generation in under a minute, contrasting with SDS methods that take over 10 minutes or longer, such as [4][43], posing challenges for users. Therefore, direct 3D generation is more practical, with 2D-lifting reserved for enhancing texture details when needed.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The procedures of our generation framework can be divide into 4 stages as shown in Fig.1 (a). Firstly, we encode the 3D objects into triplanes using the TriRenderer. The triplane encoding and TriRenderer training can be concurrently executed with only the multi-view RGBA image and camera poses as supervision. Secondly, a VAE is trained to compress the triplanes to latent space, enabling effective capture of high-level information for subsequent modules. Thirdly, a diffusion model is trained on the triplane latent code. During inference, the diffusion model produces the latent code, which can be decoded back to its corresponding triplane by the VAE decoder. Subsequently, the TriRenderer decodes the triplane into the standard GS point",
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+    {
+        "type": "page_number",
+        "text": "16230",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/0f6b3129f9dafeb1ea97a8c07c5e1e6f91700926f675d7de8e63579c4810257d.jpg",
+        "image_caption": [
+            "(a) The overall procedure of our 3D content generation framework."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/ac0245851813463f977695cdcb7376eb06ba9d71159ac02010405b1d656ef03f.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/698df0cca85d4e2868585e5d2158dea4c7d18ef59fe1938a7f12036db508cf97.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a8f4465db2ff41f986e7112ab90158b5fd05a67645196976b27a8d94f6dc0e1c.jpg",
+        "image_caption": [
+            "Figure 1. The overview of the proposed 3D GS generation framework and the core component TriRenderer. We use triplane to represent 3D objects, and design a TriRenderer to decode triplane to GS pointcloud and render multi-view images."
+        ],
+        "image_footnote": [
+            "(b) The forward pass of the TriRenderer pipeline: rendering a Triolane to multi-view images."
+        ],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "cloud. Finally, an SDS-based refiner can be utilized as an optional post-processing step to enhance or restyle the generated 3D object. Leveraging the pretrained 2D diffusion model within the SDS, the generated GS can be further improved to achieve a more detailed appearance.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1. Triplane-based GS Field",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We employ triplanes to convert the discrete multi-channel GS points into a continuous field, tailored for more efficient encoding in the subsequent generative model. Triplanes are 3 planes formed by every 2 axes of  $x,y,z$  axes in 3D space, where every 3D point  $\\mathbf{p}$  can query these planes to get corresponding features  $F_{\\mathbf{p}} = (F_{xy},F_{xz},F_{yz})$  using orthogonal projection. In real implementation, triplane is a tensor with the size of  $3\\times H\\times H\\times C$ , where  $H$  denote the resolution along every axis and  $C$  is the feature channel. The query of point with arbitrary continuous coordinate should be a bi-linear interpolation in the triplane grids. Considering GS is a set of points with multiple channels of attributes, it is natural to use triplane for GS encoding. If the triplane feature and GS attributes of a point can be transformed to each other, the sparse GS pointcloud of every object can be represented as continuous triplane GS field for further encoding. We use separate channels to encode 3D geometry and other GS attributes as described in Eq. 1, which is an experimental setting for better convergence in the training.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2. TriRenderer",
+        "text_level": 1,
+        "bbox": [
+            89,
+            832,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The TriRenderer serves as the crucial component for converting a 3D object into a triplane-based GS field. It acts as a fully differentiable bridge connecting the GS field with",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "rendering, enabling the optimization from 2D images to geometry and appearance encoding.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As depicted in Fig. 1 (b), the TriRenderer comprises a geometry branch and a GS attribute branch, each equipped with independent decoders to decode the triplane. The geometry branch is responsible for retrieve the geometry as triangular mesh from triplane, with a surface sampler for GS pointcloud sampling. Then GS attribute branch uses the obtained pointcloud to query the triplane to obtain the GS attribute corresponding to each point. In this way, the GS pointcloud in the original format is retrieved, and can be rendered using the original GS renderer. It is worth mentioning that all triplanes of different object share a common TriRenderer, which ensures the features on different triplanes subject to a similar distribution.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Geometry Branch. We use signed distance function (SDF) to represent the geometry, and allow every vertex deform as [37], so that the geometry branch decodes  $F_{p}$  to a SDF volume and its vertex deformation. By query all grid coordinates of the designated resolution  $L \\times L \\times L$ , the deformable SDF volume is reconstructed. Then we exploit a differentiable Marching Cube algorithm FlexiCubes [38] to extract triangular mesh from the SDF volume.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Surface Sampling. Considering that GS pointcloud is generally gathered on the surface of objects, we randomly sample GS points on the faces of triangular mesh with barycentric coordinates. We expect that every splat is flat and with a normal consistent with its source triangular face. Assume a face is formed by vertices  $< v_{a}, v_{b}, v_{c} >$ , and vector  $\\mathbf{v}_{1} = (v_{a} - v_{b})$ ,  $\\mathbf{v}_{2} = (v_{b} - v_{c})$ , the face normal can be calculated as  $\\mathbf{n} = \\mathbf{v}_{1} \\times \\mathbf{v}_{2}$ . Then the rotation matrix of every",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "16231",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "splat drawn from this face can be formulated as",
+        "bbox": [
+            89,
+            90,
+            406,
+            104
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {R} = \\left[ \\mathbf {v} _ {1}, \\mathbf {n} \\times \\mathbf {v} _ {1}, \\mathbf {n} \\right], \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            212,
+            116,
+            482,
+            133
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which can be transform to  $\\mathbf{q}$  in Eq.1 by standard matrix-to-quaternion algorithm. To make the splats flat,  $s_3$  in Eq.1 is fixed to an infinite small value.",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To further reduce the computational load in the subsequent GS rendering process, only faces oriented toward the camera are sampled. These face indices can be obtained through fast rasterization of the mesh faces. Note this rasterization is not required to be differentiable, and we use the library Nvdiffrast [22] for implementation.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "GS Attribute Branch. By querying the triplane GS channels with the sampled pointcloud, we can obtain the GS feature and use the GS attribute branch to transform them to the rest GS attributes. Then the GS renderer can render GS pointcloud to multi-view images. Since different GS attributes have different numerical scales and distributions, we customize individual headers to decode them respectively, which is similar to [53].",
+        "bbox": [
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+            280,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Training. The training consists of 2 stages. In the first stage, a small batch of data is used to train the triplanes and the TriRenderer together. The second stage involves the whole dataset to train all triplanes with the parameters of TriRenderer frozen. In this way, we can handle large dataset by distributed training in the second stage, and the same TriRenderer can be shared by all triplanes. There is no need to pre-train the GS pointcloud using original GS training as [21].",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The only required supervision data is  $N$  multi-view images  $\\{I_i\\}_{i=1}^N$  with camera poses, and the training losses consist of the rendering loss  $L_{\\mathrm{render}}$  and the geometric regularization  $L_{\\mathrm{geo}}$ . The rendering loss is a weighted sum as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {r e n d e r}} = w _ {1} L _ {\\text {a l p h a}} + w _ {2} L _ {\\text {r g b}} + w _ {3} L _ {\\text {p i p s}}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            143,
+            612,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $L_{\\mathrm{alpha}}$  is a  $L_{1}$  loss on the alpha map, namely the silhouette image loss;  $L_{\\mathrm{rgb}}$  is a combination of  $L_{1}$  pixel loss and SSIM loss [42] between rendered image  $\\hat{I}_i$  and ground truth  $I_i$ :",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\mathrm {r g b}} = \\sum_ {i = 1} ^ {N} (1 - \\beta) \\| I _ {i} - \\hat {I} _ {i} \\| _ {1} + \\beta \\operatorname {S S I M} \\left(I _ {i}, \\hat {I} _ {i}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "and  $L_{\\mathrm{pips}}$  is the perceptual loss [17].  $w_{1}, w_{2}, w_{3}$  and  $\\beta$  are all weighting factors determined by experiments.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The geometric regularization loss on the SDF volume  $V$  is defined as",
+        "bbox": [
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+            816
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {g e o}} = \\gamma_ {1} L _ {\\text {d e v}} + \\gamma_ {2} L _ {\\text {w e i g h t i n g}} + \\gamma_ {3} L _ {\\text {C E}} + \\gamma_ {4} L _ {\\text {s i g n}}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            102,
+            828,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the  $L_{\\mathrm{dev}}$  and  $L_{\\mathrm{weighting}}$  are defined by Flex-cubes [38] to regularize the extracted connectivity and the weighting scale of SDF vertices. To penalize the sign",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "changes on all grid edges, we follow [33] to define  $L_{\\mathrm{CE}}$  as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\mathrm {C E}} = \\sum_ {(s _ {a}, s _ {b}) \\in \\epsilon} \\operatorname {C E} \\left(\\sigma \\left(s _ {a}\\right), \\operatorname {s i g n} \\left(s _ {b}\\right)\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            581,
+            119,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where CE denotes cross entropy;  $\\epsilon$  is the set of all edges connecting vertices with different signs; and  $\\sigma$  is the sigmoid function. Finally,  $L_{\\mathrm{sign}}$  is designed to prevent the SDF volume from being trapped in an empty shape, i.e. a fully positive or fully negative SDF volume,",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {s i g n}} = \\delta (V) M (| V |), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            633,
+            239,
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+            257
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\delta (V) = 1$  if  $V$  is empty, otherwise  $\\delta (V) = 0$ .  $M(|V|)$  denotes the mean of the absolute value of  $V$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.3. Triplane VAE",
+        "text_level": 1,
+        "bbox": [
+            511,
+            301,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We employ an UNet-like structure of VAE to compress the triplane to latent space. The training pipeline is demonstrated in Fig. 2 (a). Considering that the 3 planes of triplanes encodes features from 3 orthogonal view direction, these 3 planes should be homogeneous data, so that We reshape the triplanes of batchsize  $B$  to a new batch as  $B \\times 3 \\times H \\times H \\times C$  to  $3B \\times H \\times H \\times C$  for the VAE training. We use decoupled encoders and decoders for geometry and GS channels of triplanes, for experiments prove that a mixed encoding may lead to blur of the rendering results. After the triplane is reconstructed, the TriRenderer trained in Section.4.1 can be used to retrieve the GS pointclouds and render it to images.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the training process, same loss functions as Eq. 3 and Eq. 5 are used, along with an  $L_{1}$  loss between the input and reconstructed triplanes, denoted as  $L_{\\mathrm{Tri}}$ . Additionally, a Kullback-Leibler divergence loss  $L_{\\mathrm{KL}}$  is included to ensure that the latent variables do not deviate significantly from a normal distribution. The total losses is summarized as",
+        "bbox": [
+            511,
+            520,
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+            609
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\mathrm {V A E}} = L _ {\\mathrm {T r i}} + L _ {\\mathrm {G e o}} + L _ {\\mathrm {R e n d e r}} + \\gamma L _ {\\mathrm {K L}}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            566,
+            619,
+            903,
+            636
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\gamma$  is a small weight.",
+        "bbox": [
+            511,
+            643,
+            691,
+            660
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.4. Two-stage LDM for Text-to-3D Generation",
+        "text_level": 1,
+        "bbox": [
+            511,
+            667,
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+            683
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Taking into account the significant relevance of texture appearance to the underlying geometry, we proposed to utilize staged diffusion to generate geometry and GS attribute successively as shown in Fig. 2 (b). It is easy to implement it because the latent codes for geometry and other GS attributes are totally decoupled by VAE, as mentioned earlier. In this way, the geometry code can be a new condition for the second stage.",
+        "bbox": [
+            511,
+            689,
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+            809
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We follow DDPM [12, 20] to implement the text-conditioned LDM. To better capture the relation between different planes, we roll out the triplane latent of  $B \\times 3 \\times h \\times h \\times c$  to a image-like  $B \\times 3h \\times h \\times c$  as the input of diffusion model, and the generated result will be transformed back to the original shape for TriRenderer decoding.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "16232",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/d4d455d7b936a86017daee34945deaf08686bcf6beb9a8f6ab8da1af198305b4.jpg",
+        "image_caption": [
+            "Figure 2. Triplane VAE and 2-stage diffusion."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            138,
+            87,
+            857,
+            220
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.5. SDS-based Texture Booster",
+        "text_level": 1,
+        "bbox": [
+            89,
+            275,
+            336,
+            290
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To refine or restyle the generated GS pointcloud, we utilize a pretrained 2D diffusion model for the SDS training process [35] as shown in Fig. 3. As the generated 3D GS is constrained by the mesh reconstructed from SDF, detailed in Section 4.2, we maintain the GS splats' adherence as previously established. However, we enable the mesh vertices to shift within a limited radius to enhance the stability of the SDS process. Additionally, throughout the entire SDS procedure, there is no need for densification or pruning operations. This ensures that the number of points can be controlled to align with the number of mesh faces.",
+        "bbox": [
+            89,
+            301,
+            483,
+            468
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With the image rendered from the initial GS pointcloud, the 2D diffusion model can produce images with better 2D/3D consistence in different views, so that the optimization process can converge rapidly without Janus problem.",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiment",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The experiments are conducted step-by-step according to the generation pipeline proposed as Fig.1 (a). We use OmniObject3D [45] dataset for toy experiments, and Objiverse [7] dataset for main evaluation. First, we sample 200K object to train their co顺应ing triplanes and TriNDERer. Then we train the VAE and diffusion model for 3DS GS generation. Finally, we exploit SDS to boost the texture quality for unsatisfactory generated objects. The procedure of data pre-processing and the implementation details are included in the supplementary materials.",
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+    {
+        "type": "text",
+        "text": "The experimental results primarily consist of the following components: 1) For examining the proposed triplane modeling for GS generation, we focus on the text-to-3D task and showcase the direct GS generation outcomes qualitatively and quantitatively. These results are compared with Shap-E [19], Direct3D [26], and the most recent Gaussian-Cube [52]. 2) In comparison to 2D-lifting GS generation methods, we present the performance of SDS refinement on unsatisfying samples, with GsGEN [4] and GaussianDreamer [50] as baselines.",
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+    {
+        "type": "text",
+        "text": "5.1. Triplane Fitting and VAE Reconstruction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Triplane Fitting. We adopt a resolution of  $3 \\times 128 \\times 128 \\times 16$  for all triplane fitting, with a resolution of  $64 \\times 64 \\times 64$  for the deformable SDF grids. We randomly sample 1000 objects for the shared TriRenderer training, and train all residual objects distributively. Every triplane is initialized with Gaussian noise before training. Under such settings, every triplane takes less than 30 seconds for geometry and GS appearance reconstruction.",
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+        "type": "text",
+        "text": "VAE Reconstruction. We use a down-sample factor of 4 to compress the triplanes to latent space.",
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+    {
+        "type": "text",
+        "text": "We visualize the triplane and the VAE reconstruction results of several data samples for a simple check, please refer to the supplementary materials.",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "5.2. Direct Text-to-3D GS Generation by LDM",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we present the results of our 3D GS object generation without the SDS refinement, both quantitatively and qualitatively. Due to the current scarcity of work targeting direct 3DGS generation, we selected two state-of-the-art text-to-3D works based on other 3D representations(NeRF) Shap-E [19] and Direct3D [26] for comparison. For fairness, these selected methods also perform direct generation in the 3D domain without any 2D prior knowledge or refinement based on 2D diffusion. Additionally, for the limited space, we provide more generation results and comparison with other methods such as GaussianCube [52] in the supplementary materials.",
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+    {
+        "type": "text",
+        "text": "Qualitative Results. The generation results from different methods are listed in Fig. 4. Every generated sample is rendered from different views accompanied by the provided text prompt captioned beneath the images. Our method showcase enhanced proficiency in both geometry and rendering quality, resulting in sharper and clearer outputs, which can be further verified in the subsequent quantitative evaluation. For more generated samples, please check the supplementary materials.",
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+    {
+        "type": "text",
+        "text": "Quantitative Results. We use CLIP score to evaluate the text-to-3d consistency, and an user study is conducted to evaluate the generation results from various aspect such as geometry, texture, realistic rendering and the consistency",
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+        "page_idx": 4
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+    {
+        "type": "page_number",
+        "text": "16233",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1c5fae7808bcece9143adcb3cb11fbe33f733882894530679f672ec3c79ce3e9.jpg",
+        "image_caption": [
+            "Figure 3. Score distillation process(SDS) for optional texture refinement."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/1593ef762653557dfd10d55a85de4bd7e62431342865575229bc4225a6f20f4a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Geometry↑</td><td>Texture↑</td><td>Realism↑</td><td>Consistency↑</td><td>Overall↑</td></tr><tr><td>Shap-E</td><td>3.080</td><td>3.019</td><td>2.947</td><td>3.121</td><td>3.042</td></tr><tr><td>Direct3D</td><td>3.222</td><td>3.150</td><td>3.118</td><td>3.242</td><td>3.183</td></tr><tr><td>Ours</td><td>3.456</td><td>3.383</td><td>3.332</td><td>3.520</td><td>3.423</td></tr></table>",
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+    {
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+        "table_caption": [
+            "Table 1. User study on generated 3D objects (Our results are raw outputs from LDM without SDS refinement)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Shap-E</td><td>Direct3D</td><td>Ours</td></tr><tr><td>openai:ViT-L-14</td><td>0.2398</td><td>0.2152</td><td>0.2456</td></tr><tr><td>openai:ViT-L-14-336</td><td>0.2426</td><td>0.2220</td><td>0.2462</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/43dcfffad70634b65261c29f50cd9cba3bcace2e9f15b04b62c0598dbac6ce5c.jpg",
+        "table_caption": [
+            "Table 2. CLIP score(↑) for evaluation of similarity between rendered images and given text prompt((Our results are raw outputs from LDM without SDS refinement))."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>More Realistic (%)</td><td>More Detailed (%)</td><td>Overall (%)</td></tr><tr><td>GaussianDreamer</td><td>35.0</td><td>50.0</td><td>42.5</td></tr><tr><td>GSGEN</td><td>17.5</td><td>5.0</td><td>11.3</td></tr><tr><td>Ours</td><td>47.5</td><td>45.0</td><td>46.3</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "with given prompt. 49 users participated in the user study to score the over 50 3D samples from 1 to 5 points, and the average results are shown in Tab. 1. As for the CLIP score, the open-source repository t2vmetrics [24] is used to calculate the CLIP score on two versions of ViT models, and the results are demonstrated in Tab. 2. Both the CLIP score and the user study indicate that the proposed method produces better performance.",
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+    {
+        "type": "text",
+        "text": "5.3. Optional Texture Boosting by SDS",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "To compare with other SDS-based 3D GS generation methods, we implement a version of SDS for our mesh-binding GS representation as described in Section 4.5. GsGEN [4] and GaussianDreamer [50] are selected as our baselines. The generated samples, as illustrated in Fig. 5, highlight that with the SDS refiner, our DirectTriGS can deliver competitive outcomes comparable to the state-of-the-art 2D-lifting methods.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Furthermore, we conducted a user study for quantitative evaluation. 40 users were tasked with ranking 15 samples from different methods based on two criteria: realism and level of detail. The results indicate that our approach marginally outperforms the other baseline methods.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/fd92d3b8f0105832a7be991c6cdea016b3e28d2de73d32e81c47b53873ff58b0.jpg",
+        "table_caption": [
+            "Table 3. User study on generated 3D objects (with SDS)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>TFLOPs</td><td>Paras.(M)</td><td>GPU Mem.(GB)</td><td>Running Time (Sec.)</td></tr><tr><td>Generation</td><td>0.00823</td><td>56.65</td><td>2.94</td><td>16.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Generation inference efficiency, with the batch size is 1.",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.4. Ablation Study",
+        "text_level": 1,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3D Diffusion for voxel-based Gaussian Splitting. We attempt to do GS attribute generation conditioned on given voxel occupancy via 3D diffusion model. However, even a toy experiment of over-fitting one single object failed, which may attributes to the complex multiple channels with different distributions especially the non-Euclidean ones such as quaternion. As shown in Fig.6, the diffusion model learns to generate color but fails to generate splat scaling, opacity and orientation.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Triplane Diffusion without VAE. Since VAE inherently involves a reconstruction loss, we attempt to use direct diffusion on the triplane space for generation. The experiment results show that such direct diffusion may cause serious noise on decoded geometry. Randomly generated samples are visualized in Fig.7. A possible reason is that the multichannels of triplane contain considerable noisy redundancy, which is difficult for the LDM to filter.",
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+    {
+        "type": "text",
+        "text": "Inference Efficiency. The inference efficiency is listed in Table 4. This experiment is conducted on the platform equipped with RTX3090 GPU with 24GB memory.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion & Acknowledgment",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We have presented a novel framework DirectTriGS for Gaussian Splatting Field generation. DirectTriGS mainly consists of 3 parts: 1) a light-weight triplane representation for 3D object with the format of Gaussian Splatting; 2) a fully differentiable TriRenderer which can decode triplane to original GS and render it to multi-view images; 3) the triplane VAE and staged diffusion model for the whole generation process. By utilizing our DirectTriGS, the intricate GS data can be generated directly and efficiently. 4) Additionally, we incorporate a SDS refiner to further improve the texture and details of generated objects.",
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+    {
+        "type": "text",
+        "text": "This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by NSFC-RGC Joint Fund Project N_CUHK498/24. Hongsheng Li is a PI of CPII under the InnoHK.",
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+            "(b) Comparison with Shap-E."
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+        "image_caption": [
+            "Figure 4. Comparison of generated 3D objects (Raw results without any refinement such as SDS)."
+        ],
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+    {
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+        "text": "16235",
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+    {
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+        "image_caption": [
+            "Figure 5. Refinement of unsatisfactory results by SDS, compared with pure SDS-based methods GsGEN and GaussianDreamer."
+        ],
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+        "image_caption": [
+            "Figure 6. Failure of GS attribute generation."
+        ],
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+        "image_caption": [
+            "Figure 7. Noisy results of direct diffusion on triplane. The condition prompt are \"train\", \"watermelon\" and \"box\"."
+        ],
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            91,
+            89,
+            187,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "[2] Yiwen Chen, Zilong Chen, Chi Zhang, Feng Wang, Xiaofeng Yang, Yikai Wang, Zhongang Cai, Lei Yang, Huaping Liu, and Guosheng Lin. Gaussianeditor: Swift and controllable 3d editing with gaussian splatting. arXiv preprint arXiv:2311.14521, 2023. 2",
+            "[3] Yurui Chen, Chun Gu, Junzhe Jiang, Xiatian Zhu, and Li Zhang. Periodic vibration gaussian: Dynamic urban scene reconstruction and real-time rendering. arXiv preprint arXiv:2311.18561, 2023. 2",
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2025/DirectTriGS_ Triplane-based Gaussian Splatting Field Representation for 3D Generation/cb304427-02fe-443c-baf8-93b01f1651af_model.json

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+    [
+        {
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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
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+            "bbox": [
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+            "content": "DirectTriGS: Triplane-based Gaussian Splitting Field Representation for 3D Generation"
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+            "type": "text",
+            "bbox": [
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+            "content": "Xiaoliang Ju, Hongsheng Li\\(^{1,2}\\)  \n\\(^{1}\\) CUHK MMLab \\(^{2}\\) CPII under InnoHK"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "akira@link.cuhk.edu.hk"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
+        },
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+            "bbox": [
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+            "angle": 0,
+            "content": "We present DirectTriGS, a novel framework designed for 3D object generation with Gaussian Splatting (GS). GS-based rendering for 3D content has gained considerable attention recently. However, there has been limited exploration in directly generating 3D Gaussians compared to traditional generative modeling approaches. The main challenge lies in the complex data structure of GS represented by discrete point clouds with multiple channels. To overcome this challenge, we propose employing the triplane representation, which allows us to represent Gaussian Splatting as an image-like continuous field. This representation effectively encodes both the geometry and texture information, enabling smooth transformation back to Gaussian point clouds and rendering into images by a TriRenderer, with only 2D supervisions. The proposed TriRenderer is fully differentiable, so that the rendering loss can supervise both texture and geometry encoding. Furthermore, the triplane representation can be compressed using a Variational Autoencoder (VAE), which can subsequently be utilized in latent diffusion to generate 3D objects. The experiments demonstrate that the proposed generation framework can produce high-quality 3D object geometry and rendering results in the text-to-3D task."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Neural rendering has grown to a focal point in rendering techniques in recent years, as it achieves more realistic rendering effects by leveraging the great expressiveness of neural network. The representatives are neural radiance field (NeRF) [32] and the newly emerged Gaussian Splatting (GS) [21]. However, when applied to the field of 3D generation, the slow rendering and training speed become a strong limitation for NeRF. While GS is more flexible with greater rendering efficiency and editability, few works have addressed the challenge of direct GS generation in 3D due to its complex data structure. In this paper, we propose a"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.293,
+                0.907,
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+            ],
+            "angle": 0,
+            "content": "novel approach called DirectTriGS, which encodes GS as triplane representation, and introduce its corresponding renderer, TriRenderer. Subsequently, we apply latent diffusion on the Triplane representation to generate high-quality GS objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Gaussian splatting uses multi-channel point cloud of \"splats\" to describe the 3D contents. With a differentiable splats rasterizer, GS has fast rendering speed. However, the sparsity, multiple channels, and uneven distributed density of 3D GS bring great difficulty for 3D generation. We propose to encode GS contents as multi-channel triplane representations, which have been shown to possess favorable properties for representing 3D geometry or NeRF, as demonstrated in previous works Shue et al. [40], Wu et al. [47]. In our work, we leverage the triplane representation to encode both the geometry information and other GS attributes in two separate groups of channels. By training on a dataset of 3D objects, we obtain a shared TriRenderer that is capable of decoding different triplane representations to GS and then render it to image. TriRenderer is fully differentiable, enabling the use of only 2D rendering loss to supervise both the texture and geometry of 3D GS. The advantage of using Triplane to represent GS are two folds. First, it leads to high memory efficiency compared with dense voxels and is expressive enough for generating various 3D GS. Second, Triplane is more compatible with the convolution-based encoders compared with the original sparse GS point cloud, which require specifically designed networks on processing sparse point clouds."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.735,
+                0.911,
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+            ],
+            "angle": 0,
+            "content": "We follow stable diffusion [36] to train DirectTriGS on the proposed triplane representation. Specifically, a VAE is designed to further convert the Triplanes into latent code. We use two separate decoders to decouple the decoding of geometry and GS attributes. Second, we roll out the triplane latent to an expanded multi-channel image, then exploit staged latent diffusion to do generation. Two-stage diffusion is employed to generate the geometry and the corresponding GS appearance. Finally, score distillation sampling (SDS) [35] is adopted as a optional post-processing to refine or restyle the generated 3D objects."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "16229"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.482,
+                0.272
+            ],
+            "angle": 0,
+            "content": "Our contribution can summarize as follows. 1) We propose a Triplane representation for direct 3D GS generation, which is memory efficient to derive GS point clouds with vivid rendering. 2) We design a fully differentiable TriRenderer to enable the end-to-end training of triplane representations, with only 2D supervisions. 3) We develop a Triplane-based GS generation framework DirectTriGS that incorporates a specially designed VAE, latent diffusion module, and a SDS based refiner. 4) Experiments demonstrate our method produces competitive performance in both 3D geometry and multi-view rendering quality in text-to-3D tasks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.287,
+                0.24,
+                0.303
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.312,
+                0.483,
+                0.568
+            ],
+            "angle": 0,
+            "content": "3D Object Generation. 1) Multi-view images-to-3D. The first route generates multi-view colored 3D image and then reconstruct the 3D shape and project image to texture, or use score distillation sampling to build 3D object from images produced by 2D diffusion, such as [6, 13, 27, 35, 39, 41]. Since these approaches are actually 2D generator, it is difficult to maintain 3D consistency, which may lead to Janus problem. 2) Image-to-3D. The second route attempt to retrieve 3D geometry from a single input image, such as [25, 28, 53]. With the certain one image as input, the users may be more concerned with the reconstruction quality. 3)Text-to-3D. The third group mainly operate in 3D, which can be clustered by different 3D representation. For example, [10, 11] are able to generate high-quality 3D textured meshes using differentiable rendering; [34, 46] generate colored pointcloud; [1, 14, 23, 31] generate NeRF volumes; [18, 47] generate SDF volumes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.569,
+                0.483,
+                0.629
+            ],
+            "angle": 0,
+            "content": "Remark. The input conditions of these three generation methods are gradually becoming abstract, corresponding to increasing difficulty of the generation task, commonly resulting in a gradual decline in the generation quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.63,
+                0.483,
+                0.75
+            ],
+            "angle": 0,
+            "content": "Gaussian Splatting. Gaussian Splatting [21] exploits multi-channel pointcloud of splats to describe the 3D content, which allows real-time rendering of photorealistic scenes. Recently, there emerges so many research focusing on its reconstruction quality enhancement and algorithm optimization [5, 8, 15, 29, 51]. Another related active area includes 4D dynamic GS modeling [3, 44, 49], scene editing [2, 9] and its applications like SLAM [30, 48]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.751,
+                0.483,
+                0.902
+            ],
+            "angle": 0,
+            "content": "As for GS generation, some works exploit multi-view image based route such as [6, 41], where the image generator output image from required views to enhance the GS rendering in a recursive manner. Rare works explore the GS generation directly in 3D space, such as [53] generates a point cloud using a Transformer structure with 2D image as input, and build a mapping of image to tri-plane encoding of GS attribute; GaussianCube [52] proposes to use optimal transport to model the 3D GS for text-to-3D generation; [16] combine explicit anchor points with implicit"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.092,
+                0.772,
+                0.108
+            ],
+            "angle": 0,
+            "content": "triplane to directly generate GS points."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.119,
+                0.787,
+                0.137
+            ],
+            "angle": 0,
+            "content": "3. Revisiting Gaussian Splitting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.145,
+                0.905,
+                0.298
+            ],
+            "angle": 0,
+            "content": "Gaussian Splatting [21] uses a set of Gaussian points to describe a 3D object. The Gaussian points are defined by a full 3D covariance matrix \\(\\pmb{\\Sigma}\\) in a world space as \\(G(\\mathbf{x}) = e^{-\\frac{1}{2}\\mathbf{x}^T\\pmb{\\Sigma}^{-1}\\mathbf{x}}\\), centered at point (mean) \\(\\mathbf{p} \\in \\mathbb{R}^3\\). Each point is with a opacity scalar \\(\\alpha \\in [0,1]\\) for blending and a series of Spherical Harmonics (SH) coefficients to correctly capture the view-dependent appearance of the scene. The number of SH coefficients are \\(3 \\times (n + 1)^2\\), where \\(n\\) denotes the SH order, and higher \\(n\\) corresponds to more accurate view-dependent appearance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.298,
+                0.906,
+                0.449
+            ],
+            "angle": 0,
+            "content": "During rendering, the Gaussians are project to 2D given a viewing transformation \\(\\mathbf{W}\\). The covariance is transformed as \\(\\boldsymbol{\\Sigma}^{\\prime} = \\mathbf{J}\\mathbf{W}\\boldsymbol{\\Sigma}\\mathbf{W}^{T}\\mathbf{J}^{T}\\), where \\(\\mathbf{J}\\) is the Jacobian of the affine approximation of the projective transformation. To ensure \\(\\boldsymbol{\\Sigma}\\) to be semi-positive in the whole training process, \\(\\boldsymbol{\\Sigma}\\) can be represented by a Cholesky decomposition as \\(\\boldsymbol{\\Sigma} = \\mathbf{R}\\mathbf{S}\\mathbf{S}^{T}\\mathbf{R}^{T}\\), represented by a tuple \\(s = (s_{1}, s_{2}, s_{3})\\) for scaling and a unnormalized quaternion \\(\\mathbf{q} \\in \\mathbb{R}^{4}\\) for rotation. In summary, each Gaussian point are a union set of position \\(\\mathbf{p}\\) and its GS attributes:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.638,
+                0.459,
+                0.905,
+                0.476
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {G} _ {\\mathbf {p}} := \\{s, \\mathbf {q}, \\mathrm {S H}, \\alpha \\}. \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.485,
+                0.904,
+                0.516
+            ],
+            "angle": 0,
+            "content": "GS pointcloud can be efficiently rendered by a rasterization-based splatting renderer [21], which is fully differentiable."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.529,
+                0.649,
+                0.546
+            ],
+            "angle": 0,
+            "content": "4. Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.553,
+                0.906,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Our motivation is to directly generate 3D GS with fast speed by utilizing the proposed triplane-based GS representation. While 2D-lifting methods like SDS-based approaches yield intricate results, they are time-intensive and susceptible to Janus problem. Direct generation, notably with fast sampling, can complete 3D generation in under a minute, contrasting with SDS methods that take over 10 minutes or longer, such as [4][43], posing challenges for users. Therefore, direct 3D generation is more practical, with 2D-lifting reserved for enhancing texture details when needed."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.705,
+                0.907,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The procedures of our generation framework can be divide into 4 stages as shown in Fig.1 (a). Firstly, we encode the 3D objects into triplanes using the TriRenderer. The triplane encoding and TriRenderer training can be concurrently executed with only the multi-view RGBA image and camera poses as supervision. Secondly, a VAE is trained to compress the triplanes to latent space, enabling effective capture of high-level information for subsequent modules. Thirdly, a diffusion model is trained on the triplane latent code. During inference, the diffusion model produces the latent code, which can be decoded back to its corresponding triplane by the VAE decoder. Subsequently, the TriRenderer decodes the triplane into the standard GS point"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16230"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.137,
+                0.09,
+                0.308,
+                0.143
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.322,
+                0.091,
+                0.493,
+                0.143
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.506,
+                0.091,
+                0.678,
+                0.143
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.691,
+                0.092,
+                0.863,
+                0.143
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.304,
+                0.149,
+                0.66,
+                0.163
+            ],
+            "angle": 0,
+            "content": "(a) The overall procedure of our 3D content generation framework."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.135,
+                0.172,
+                0.863,
+                0.345
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_footnote",
+            "bbox": [
+                0.262,
+                0.349,
+                0.747,
+                0.361
+            ],
+            "angle": 0,
+            "content": "(b) The forward pass of the TriRenderer pipeline: rendering a Triolane to multi-view images."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.371,
+                0.908,
+                0.399
+            ],
+            "angle": 0,
+            "content": "Figure 1. The overview of the proposed 3D GS generation framework and the core component TriRenderer. We use triplane to represent 3D objects, and design a TriRenderer to decode triplane to GS pointcloud and render multi-view images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.426,
+                0.484,
+                0.501
+            ],
+            "angle": 0,
+            "content": "cloud. Finally, an SDS-based refiner can be utilized as an optional post-processing step to enhance or restyle the generated 3D object. Leveraging the pretrained 2D diffusion model within the SDS, the generated GS can be further improved to achieve a more detailed appearance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.512,
+                0.315,
+                0.528
+            ],
+            "angle": 0,
+            "content": "4.1. Triplane-based GS Field"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.535,
+                0.484,
+                0.822
+            ],
+            "angle": 0,
+            "content": "We employ triplanes to convert the discrete multi-channel GS points into a continuous field, tailored for more efficient encoding in the subsequent generative model. Triplanes are 3 planes formed by every 2 axes of \\(x,y,z\\) axes in 3D space, where every 3D point \\(\\mathbf{p}\\) can query these planes to get corresponding features \\(F_{\\mathbf{p}} = (F_{xy},F_{xz},F_{yz})\\) using orthogonal projection. In real implementation, triplane is a tensor with the size of \\(3\\times H\\times H\\times C\\), where \\(H\\) denote the resolution along every axis and \\(C\\) is the feature channel. The query of point with arbitrary continuous coordinate should be a bi-linear interpolation in the triplane grids. Considering GS is a set of points with multiple channels of attributes, it is natural to use triplane for GS encoding. If the triplane feature and GS attributes of a point can be transformed to each other, the sparse GS pointcloud of every object can be represented as continuous triplane GS field for further encoding. We use separate channels to encode 3D geometry and other GS attributes as described in Eq. 1, which is an experimental setting for better convergence in the training."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.833,
+                0.224,
+                0.848
+            ],
+            "angle": 0,
+            "content": "4.2. TriRenderer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.856,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The TriRenderer serves as the crucial component for converting a 3D object into a triplane-based GS field. It acts as a fully differentiable bridge connecting the GS field with"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.426,
+                0.905,
+                0.456
+            ],
+            "angle": 0,
+            "content": "rendering, enabling the optimization from 2D images to geometry and appearance encoding."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.458,
+                0.907,
+                0.655
+            ],
+            "angle": 0,
+            "content": "As depicted in Fig. 1 (b), the TriRenderer comprises a geometry branch and a GS attribute branch, each equipped with independent decoders to decode the triplane. The geometry branch is responsible for retrieve the geometry as triangular mesh from triplane, with a surface sampler for GS pointcloud sampling. Then GS attribute branch uses the obtained pointcloud to query the triplane to obtain the GS attribute corresponding to each point. In this way, the GS pointcloud in the original format is retrieved, and can be rendered using the original GS renderer. It is worth mentioning that all triplanes of different object share a common TriRenderer, which ensures the features on different triplanes subject to a similar distribution."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.657,
+                0.906,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Geometry Branch. We use signed distance function (SDF) to represent the geometry, and allow every vertex deform as [37], so that the geometry branch decodes \\( F_{p} \\) to a SDF volume and its vertex deformation. By query all grid coordinates of the designated resolution \\( L \\times L \\times L \\), the deformable SDF volume is reconstructed. Then we exploit a differentiable Marching Cube algorithm FlexiCubes [38] to extract triangular mesh from the SDF volume."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.78,
+                0.909,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Surface Sampling. Considering that GS pointcloud is generally gathered on the surface of objects, we randomly sample GS points on the faces of triangular mesh with barycentric coordinates. We expect that every splat is flat and with a normal consistent with its source triangular face. Assume a face is formed by vertices \\( < v_{a}, v_{b}, v_{c} > \\), and vector \\( \\mathbf{v}_{1} = (v_{a} - v_{b}) \\), \\( \\mathbf{v}_{2} = (v_{b} - v_{c}) \\), the face normal can be calculated as \\( \\mathbf{n} = \\mathbf{v}_{1} \\times \\mathbf{v}_{2} \\). Then the rotation matrix of every"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16231"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.092,
+                0.407,
+                0.106
+            ],
+            "angle": 0,
+            "content": "splat drawn from this face can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.213,
+                0.117,
+                0.483,
+                0.134
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {R} = \\left[ \\mathbf {v} _ {1}, \\mathbf {n} \\times \\mathbf {v} _ {1}, \\mathbf {n} \\right], \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.145,
+                0.483,
+                0.189
+            ],
+            "angle": 0,
+            "content": "which can be transform to \\(\\mathbf{q}\\) in Eq.1 by standard matrix-to-quaternion algorithm. To make the splats flat, \\(s_3\\) in Eq.1 is fixed to an infinite small value."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.19,
+                0.484,
+                0.281
+            ],
+            "angle": 0,
+            "content": "To further reduce the computational load in the subsequent GS rendering process, only faces oriented toward the camera are sampled. These face indices can be obtained through fast rasterization of the mesh faces. Note this rasterization is not required to be differentiable, and we use the library Nvdiffrast [22] for implementation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.281,
+                0.484,
+                0.401
+            ],
+            "angle": 0,
+            "content": "GS Attribute Branch. By querying the triplane GS channels with the sampled pointcloud, we can obtain the GS feature and use the GS attribute branch to transform them to the rest GS attributes. Then the GS renderer can render GS pointcloud to multi-view images. Since different GS attributes have different numerical scales and distributions, we customize individual headers to decode them respectively, which is similar to [53]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.402,
+                0.484,
+                0.538
+            ],
+            "angle": 0,
+            "content": "Training. The training consists of 2 stages. In the first stage, a small batch of data is used to train the triplanes and the TriRenderer together. The second stage involves the whole dataset to train all triplanes with the parameters of TriRenderer frozen. In this way, we can handle large dataset by distributed training in the second stage, and the same TriRenderer can be shared by all triplanes. There is no need to pre-train the GS pointcloud using original GS training as [21]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.538,
+                0.484,
+                0.599
+            ],
+            "angle": 0,
+            "content": "The only required supervision data is \\(N\\) multi-view images \\(\\{I_i\\}_{i=1}^N\\) with camera poses, and the training losses consist of the rendering loss \\(L_{\\mathrm{render}}\\) and the geometric regularization \\(L_{\\mathrm{geo}}\\). The rendering loss is a weighted sum as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.144,
+                0.613,
+                0.483,
+                0.629
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {r e n d e r}} = w _ {1} L _ {\\text {a l p h a}} + w _ {2} L _ {\\text {r g b}} + w _ {3} L _ {\\text {p i p s}}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.635,
+                0.484,
+                0.697
+            ],
+            "angle": 0,
+            "content": "where \\( L_{\\mathrm{alpha}} \\) is a \\( L_{1} \\) loss on the alpha map, namely the silhouette image loss; \\( L_{\\mathrm{rgb}} \\) is a combination of \\( L_{1} \\) pixel loss and SSIM loss [42] between rendered image \\( \\hat{I}_i \\) and ground truth \\( I_i \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.118,
+                0.706,
+                0.483,
+                0.749
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\mathrm {r g b}} = \\sum_ {i = 1} ^ {N} (1 - \\beta) \\| I _ {i} - \\hat {I} _ {i} \\| _ {1} + \\beta \\operatorname {S S I M} \\left(I _ {i}, \\hat {I} _ {i}\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.757,
+                0.483,
+                0.787
+            ],
+            "angle": 0,
+            "content": "and \\(L_{\\mathrm{pips}}\\) is the perceptual loss [17]. \\(w_{1}, w_{2}, w_{3}\\) and \\(\\beta\\) are all weighting factors determined by experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.787,
+                0.484,
+                0.817
+            ],
+            "angle": 0,
+            "content": "The geometric regularization loss on the SDF volume \\(V\\) is defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.104,
+                0.829,
+                0.483,
+                0.846
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {g e o}} = \\gamma_ {1} L _ {\\text {d e v}} + \\gamma_ {2} L _ {\\text {w e i g h t i n g}} + \\gamma_ {3} L _ {\\text {C E}} + \\gamma_ {4} L _ {\\text {s i g n}}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.856,
+                0.484,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where the \\(L_{\\mathrm{dev}}\\) and \\(L_{\\mathrm{weighting}}\\) are defined by Flex-cubes [38] to regularize the extracted connectivity and the weighting scale of SDF vertices. To penalize the sign"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.092,
+                0.905,
+                0.12
+            ],
+            "angle": 0,
+            "content": "changes on all grid edges, we follow [33] to define \\(L_{\\mathrm{CE}}\\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.583,
+                0.12,
+                0.905,
+                0.153
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\mathrm {C E}} = \\sum_ {(s _ {a}, s _ {b}) \\in \\epsilon} \\operatorname {C E} \\left(\\sigma \\left(s _ {a}\\right), \\operatorname {s i g n} \\left(s _ {b}\\right)\\right), \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.156,
+                0.907,
+                0.232
+            ],
+            "angle": 0,
+            "content": "where CE denotes cross entropy; \\(\\epsilon\\) is the set of all edges connecting vertices with different signs; and \\(\\sigma\\) is the sigmoid function. Finally, \\(L_{\\mathrm{sign}}\\) is designed to prevent the SDF volume from being trapped in an empty shape, i.e. a fully positive or fully negative SDF volume,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.634,
+                0.24,
+                0.905,
+                0.258
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {s i g n}} = \\delta (V) M (| V |), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.264,
+                0.905,
+                0.296
+            ],
+            "angle": 0,
+            "content": "where \\(\\delta (V) = 1\\) if \\(V\\) is empty, otherwise \\(\\delta (V) = 0\\). \\(M(|V|)\\) denotes the mean of the absolute value of \\(V\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.303,
+                0.657,
+                0.319
+            ],
+            "angle": 0,
+            "content": "4.3. Triplane VAE"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.325,
+                0.907,
+                0.521
+            ],
+            "angle": 0,
+            "content": "We employ an UNet-like structure of VAE to compress the triplane to latent space. The training pipeline is demonstrated in Fig. 2 (a). Considering that the 3 planes of triplanes encodes features from 3 orthogonal view direction, these 3 planes should be homogeneous data, so that We reshape the triplanes of batchsize \\( B \\) to a new batch as \\( B \\times 3 \\times H \\times H \\times C \\) to \\( 3B \\times H \\times H \\times C \\) for the VAE training. We use decoupled encoders and decoders for geometry and GS channels of triplanes, for experiments prove that a mixed encoding may lead to blur of the rendering results. After the triplane is reconstructed, the TriRenderer trained in Section.4.1 can be used to retrieve the GS pointclouds and render it to images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.521,
+                0.906,
+                0.611
+            ],
+            "angle": 0,
+            "content": "In the training process, same loss functions as Eq. 3 and Eq. 5 are used, along with an \\( L_{1} \\) loss between the input and reconstructed triplanes, denoted as \\( L_{\\mathrm{Tri}} \\). Additionally, a Kullback-Leibler divergence loss \\( L_{\\mathrm{KL}} \\) is included to ensure that the latent variables do not deviate significantly from a normal distribution. The total losses is summarized as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.568,
+                0.621,
+                0.905,
+                0.637
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\mathrm {V A E}} = L _ {\\mathrm {T r i}} + L _ {\\mathrm {G e o}} + L _ {\\mathrm {R e n d e r}} + \\gamma L _ {\\mathrm {K L}}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.645,
+                0.692,
+                0.661
+            ],
+            "angle": 0,
+            "content": "where \\(\\gamma\\) is a small weight."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.668,
+                0.879,
+                0.684
+            ],
+            "angle": 0,
+            "content": "4.4. Two-stage LDM for Text-to-3D Generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.69,
+                0.906,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Taking into account the significant relevance of texture appearance to the underlying geometry, we proposed to utilize staged diffusion to generate geometry and GS attribute successively as shown in Fig. 2 (b). It is easy to implement it because the latent codes for geometry and other GS attributes are totally decoupled by VAE, as mentioned earlier. In this way, the geometry code can be a new condition for the second stage."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.811,
+                0.906,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We follow DDPM [12, 20] to implement the text-conditioned LDM. To better capture the relation between different planes, we roll out the triplane latent of \\( B \\times 3 \\times h \\times h \\times c \\) to a image-like \\( B \\times 3h \\times h \\times c \\) as the input of diffusion model, and the generated result will be transformed back to the original shape for TriRenderer decoding."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16232"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.139,
+                0.088,
+                0.858,
+                0.222
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.36,
+                0.235,
+                0.637,
+                0.25
+            ],
+            "angle": 0,
+            "content": "Figure 2. Triplane VAE and 2-stage diffusion."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.276,
+                0.338,
+                0.291
+            ],
+            "angle": 0,
+            "content": "4.5. SDS-based Texture Booster"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.303,
+                0.484,
+                0.469
+            ],
+            "angle": 0,
+            "content": "To refine or restyle the generated GS pointcloud, we utilize a pretrained 2D diffusion model for the SDS training process [35] as shown in Fig. 3. As the generated 3D GS is constrained by the mesh reconstructed from SDF, detailed in Section 4.2, we maintain the GS splats' adherence as previously established. However, we enable the mesh vertices to shift within a limited radius to enhance the stability of the SDS process. Additionally, throughout the entire SDS procedure, there is no need for densification or pruning operations. This ensures that the number of points can be controlled to align with the number of mesh faces."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.474,
+                0.484,
+                0.536
+            ],
+            "angle": 0,
+            "content": "With the image rendered from the initial GS pointcloud, the 2D diffusion model can produce images with better 2D/3D consistence in different views, so that the optimization process can converge rapidly without Janus problem."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.564,
+                0.216,
+                0.58
+            ],
+            "angle": 0,
+            "content": "5. Experiment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.594,
+                0.483,
+                0.746
+            ],
+            "angle": 0,
+            "content": "The experiments are conducted step-by-step according to the generation pipeline proposed as Fig.1 (a). We use OmniObject3D [45] dataset for toy experiments, and Objiverse [7] dataset for main evaluation. First, we sample 200K object to train their co顺应ing triplanes and TriNDERer. Then we train the VAE and diffusion model for 3DS GS generation. Finally, we exploit SDS to boost the texture quality for unsatisfactory generated objects. The procedure of data pre-processing and the implementation details are included in the supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.75,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The experimental results primarily consist of the following components: 1) For examining the proposed triplane modeling for GS generation, we focus on the text-to-3D task and showcase the direct GS generation outcomes qualitatively and quantitatively. These results are compared with Shap-E [19], Direct3D [26], and the most recent Gaussian-Cube [52]. 2) In comparison to 2D-lifting GS generation methods, we present the performance of SDS refinement on unsatisfying samples, with GsGEN [4] and GaussianDreamer [50] as baselines."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.276,
+                0.868,
+                0.293
+            ],
+            "angle": 0,
+            "content": "5.1. Triplane Fitting and VAE Reconstruction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.298,
+                0.905,
+                0.418
+            ],
+            "angle": 0,
+            "content": "Triplane Fitting. We adopt a resolution of \\(3 \\times 128 \\times 128 \\times 16\\) for all triplane fitting, with a resolution of \\(64 \\times 64 \\times 64\\) for the deformable SDF grids. We randomly sample 1000 objects for the shared TriRenderer training, and train all residual objects distributively. Every triplane is initialized with Gaussian noise before training. Under such settings, every triplane takes less than 30 seconds for geometry and GS appearance reconstruction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.419,
+                0.905,
+                0.449
+            ],
+            "angle": 0,
+            "content": "VAE Reconstruction. We use a down-sample factor of 4 to compress the triplanes to latent space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.45,
+                0.905,
+                0.495
+            ],
+            "angle": 0,
+            "content": "We visualize the triplane and the VAE reconstruction results of several data samples for a simple check, please refer to the supplementary materials."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.502,
+                0.874,
+                0.518
+            ],
+            "angle": 0,
+            "content": "5.2. Direct Text-to-3D GS Generation by LDM"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.524,
+                0.906,
+                0.704
+            ],
+            "angle": 0,
+            "content": "In this section, we present the results of our 3D GS object generation without the SDS refinement, both quantitatively and qualitatively. Due to the current scarcity of work targeting direct 3DGS generation, we selected two state-of-the-art text-to-3D works based on other 3D representations(NeRF) Shap-E [19] and Direct3D [26] for comparison. For fairness, these selected methods also perform direct generation in the 3D domain without any 2D prior knowledge or refinement based on 2D diffusion. Additionally, for the limited space, we provide more generation results and comparison with other methods such as GaussianCube [52] in the supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.705,
+                0.906,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Qualitative Results. The generation results from different methods are listed in Fig. 4. Every generated sample is rendered from different views accompanied by the provided text prompt captioned beneath the images. Our method showcase enhanced proficiency in both geometry and rendering quality, resulting in sharper and clearer outputs, which can be further verified in the subsequent quantitative evaluation. For more generated samples, please check the supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.841,
+                0.905,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Quantitative Results. We use CLIP score to evaluate the text-to-3d consistency, and an user study is conducted to evaluate the generation results from various aspect such as geometry, texture, realistic rendering and the consistency"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16233"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.154,
+                0.091,
+                0.825,
+                0.144
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.281,
+                0.155,
+                0.715,
+                0.171
+            ],
+            "angle": 0,
+            "content": "Figure 3. Score distillation process(SDS) for optional texture refinement."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.095,
+                0.186,
+                0.48,
+                0.245
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Geometry↑</td><td>Texture↑</td><td>Realism↑</td><td>Consistency↑</td><td>Overall↑</td></tr><tr><td>Shap-E</td><td>3.080</td><td>3.019</td><td>2.947</td><td>3.121</td><td>3.042</td></tr><tr><td>Direct3D</td><td>3.222</td><td>3.150</td><td>3.118</td><td>3.242</td><td>3.183</td></tr><tr><td>Ours</td><td>3.456</td><td>3.383</td><td>3.332</td><td>3.520</td><td>3.423</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.255,
+                0.483,
+                0.283
+            ],
+            "angle": 0,
+            "content": "Table 1. User study on generated 3D objects (Our results are raw outputs from LDM without SDS refinement)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.107,
+                0.305,
+                0.47,
+                0.366
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Shap-E</td><td>Direct3D</td><td>Ours</td></tr><tr><td>openai:ViT-L-14</td><td>0.2398</td><td>0.2152</td><td>0.2456</td></tr><tr><td>openai:ViT-L-14-336</td><td>0.2426</td><td>0.2220</td><td>0.2462</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.376,
+                0.484,
+                0.418
+            ],
+            "angle": 0,
+            "content": "Table 2. CLIP score(↑) for evaluation of similarity between rendered images and given text prompt((Our results are raw outputs from LDM without SDS refinement))."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.105,
+                0.44,
+                0.472,
+                0.496
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>More Realistic (%)</td><td>More Detailed (%)</td><td>Overall (%)</td></tr><tr><td>GaussianDreamer</td><td>35.0</td><td>50.0</td><td>42.5</td></tr><tr><td>GSGEN</td><td>17.5</td><td>5.0</td><td>11.3</td></tr><tr><td>Ours</td><td>47.5</td><td>45.0</td><td>46.3</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.117,
+                0.506,
+                0.456,
+                0.521
+            ],
+            "angle": 0,
+            "content": "Table 3. User study on generated 3D objects (with SDS)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.531,
+                0.484,
+                0.651
+            ],
+            "angle": 0,
+            "content": "with given prompt. 49 users participated in the user study to score the over 50 3D samples from 1 to 5 points, and the average results are shown in Tab. 1. As for the CLIP score, the open-source repository t2vmetrics [24] is used to calculate the CLIP score on two versions of ViT models, and the results are demonstrated in Tab. 2. Both the CLIP score and the user study indicate that the proposed method produces better performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.673,
+                0.391,
+                0.691
+            ],
+            "angle": 0,
+            "content": "5.3. Optional Texture Boosting by SDS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.7,
+                0.483,
+                0.82
+            ],
+            "angle": 0,
+            "content": "To compare with other SDS-based 3D GS generation methods, we implement a version of SDS for our mesh-binding GS representation as described in Section 4.5. GsGEN [4] and GaussianDreamer [50] are selected as our baselines. The generated samples, as illustrated in Fig. 5, highlight that with the SDS refiner, our DirectTriGS can deliver competitive outcomes comparable to the state-of-the-art 2D-lifting methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.826,
+                0.484,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Furthermore, we conducted a user study for quantitative evaluation. 40 users were tasked with ranking 15 samples from different methods based on two criteria: realism and level of detail. The results indicate that our approach marginally outperforms the other baseline methods."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.518,
+                0.186,
+                0.905,
+                0.218
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>TFLOPs</td><td>Paras.(M)</td><td>GPU Mem.(GB)</td><td>Running Time (Sec.)</td></tr><tr><td>Generation</td><td>0.00823</td><td>56.65</td><td>2.94</td><td>16.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.516,
+                0.227,
+                0.901,
+                0.241
+            ],
+            "angle": 0,
+            "content": "Table 4. Generation inference efficiency, with the batch size is 1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.249,
+                0.667,
+                0.266
+            ],
+            "angle": 0,
+            "content": "5.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.271,
+                0.907,
+                0.407
+            ],
+            "angle": 0,
+            "content": "3D Diffusion for voxel-based Gaussian Splitting. We attempt to do GS attribute generation conditioned on given voxel occupancy via 3D diffusion model. However, even a toy experiment of over-fitting one single object failed, which may attributes to the complex multiple channels with different distributions especially the non-Euclidean ones such as quaternion. As shown in Fig.6, the diffusion model learns to generate color but fails to generate splat scaling, opacity and orientation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.407,
+                0.906,
+                0.527
+            ],
+            "angle": 0,
+            "content": "Triplane Diffusion without VAE. Since VAE inherently involves a reconstruction loss, we attempt to use direct diffusion on the triplane space for generation. The experiment results show that such direct diffusion may cause serious noise on decoded geometry. Randomly generated samples are visualized in Fig.7. A possible reason is that the multichannels of triplane contain considerable noisy redundancy, which is difficult for the LDM to filter."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.528,
+                0.906,
+                0.575
+            ],
+            "angle": 0,
+            "content": "Inference Efficiency. The inference efficiency is listed in Table 4. This experiment is conducted on the platform equipped with RTX3090 GPU with 24GB memory."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.587,
+                0.805,
+                0.605
+            ],
+            "angle": 0,
+            "content": "6. Conclusion & Acknowledgment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.612,
+                0.907,
+                0.779
+            ],
+            "angle": 0,
+            "content": "We have presented a novel framework DirectTriGS for Gaussian Splatting Field generation. DirectTriGS mainly consists of 3 parts: 1) a light-weight triplane representation for 3D object with the format of Gaussian Splatting; 2) a fully differentiable TriRenderer which can decode triplane to original GS and render it to multi-view images; 3) the triplane VAE and staged diffusion model for the whole generation process. By utilizing our DirectTriGS, the intricate GS data can be generated directly and efficiently. 4) Additionally, we incorporate a SDS refiner to further improve the texture and details of generated objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.779,
+                0.909,
+                0.899
+            ],
+            "angle": 0,
+            "content": "This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by NSFC-RGC Joint Fund Project N_CUHK498/24. Hongsheng Li is a PI of CPII under the InnoHK."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "16234"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": null
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+            "bbox": [
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+            "angle": 0,
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+        {
+            "type": "image",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.868,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.407,
+                0.427,
+                0.589,
+                0.44
+            ],
+            "angle": 0,
+            "content": "(a) Comparison with Direct3D."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.111,
+                0.463,
+                0.355,
+                0.584
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.464,
+                0.612,
+                0.58
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.626,
+                0.463,
+                0.888,
+                0.584
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.588,
+                0.351,
+                0.81
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.588,
+                0.625,
+                0.81
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.644,
+                0.589,
+                0.882,
+                0.813
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.407,
+                0.82,
+                0.581,
+                0.834
+            ],
+            "angle": 0,
+            "content": "(b) Comparison with Shap-E."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.2,
+                0.868,
+                0.798,
+                0.882
+            ],
+            "angle": 0,
+            "content": "Figure 4. Comparison of generated 3D objects (Raw results without any refinement such as SDS)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16235"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.162,
+                0.088,
+                0.824,
+                0.684
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.119,
+                0.692,
+                0.879,
+                0.708
+            ],
+            "angle": 0,
+            "content": "Figure 5. Refinement of unsatisfactory results by SDS, compared with pure SDS-based methods GsGEN and GaussianDreamer."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.186,
+                0.735,
+                0.33,
+                0.83
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.167,
+                0.845,
+                0.349,
+                0.873
+            ],
+            "angle": 0,
+            "content": "Figure 6. Failure of GS attribute generation."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.366,
+                0.737,
+                0.83,
+                0.828
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.364,
+                0.841,
+                0.83,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Figure 7. Noisy results of direct diffusion on triplane. The condition prompt are \"train\", \"watermelon\" and \"box\"."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.946,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16236"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.093,
+                0.09,
+                0.188,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.101,
+                0.115,
+                0.484,
+                0.184
+            ],
+            "angle": 0,
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+        {
+            "type": "ref_text",
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+    ]
+]

2025/DirectTriGS_ Triplane-based Gaussian Splatting Field Representation for 3D Generation/cb304427-02fe-443c-baf8-93b01f1651af_origin.pdf

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2025/DirectTriGS_ Triplane-based Gaussian Splatting Field Representation for 3D Generation/full.md

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+# DirectTriGS: Triplane-based Gaussian Splitting Field Representation for 3D Generation
+
+Xiaoliang Ju, Hongsheng Li $^{1,2}$ $^{1}$  CUHK MMLab  $^{2}$  CPII under InnoHK
+
+akira@link.cuhk.edu.hk
+
+# Abstract
+
+We present DirectTriGS, a novel framework designed for 3D object generation with Gaussian Splatting (GS). GS-based rendering for 3D content has gained considerable attention recently. However, there has been limited exploration in directly generating 3D Gaussians compared to traditional generative modeling approaches. The main challenge lies in the complex data structure of GS represented by discrete point clouds with multiple channels. To overcome this challenge, we propose employing the triplane representation, which allows us to represent Gaussian Splatting as an image-like continuous field. This representation effectively encodes both the geometry and texture information, enabling smooth transformation back to Gaussian point clouds and rendering into images by a TriRenderer, with only 2D supervisions. The proposed TriRenderer is fully differentiable, so that the rendering loss can supervise both texture and geometry encoding. Furthermore, the triplane representation can be compressed using a Variational Autoencoder (VAE), which can subsequently be utilized in latent diffusion to generate 3D objects. The experiments demonstrate that the proposed generation framework can produce high-quality 3D object geometry and rendering results in the text-to-3D task.
+
+# 1. Introduction
+
+Neural rendering has grown to a focal point in rendering techniques in recent years, as it achieves more realistic rendering effects by leveraging the great expressiveness of neural network. The representatives are neural radiance field (NeRF) [32] and the newly emerged Gaussian Splatting (GS) [21]. However, when applied to the field of 3D generation, the slow rendering and training speed become a strong limitation for NeRF. While GS is more flexible with greater rendering efficiency and editability, few works have addressed the challenge of direct GS generation in 3D due to its complex data structure. In this paper, we propose a
+
+novel approach called DirectTriGS, which encodes GS as triplane representation, and introduce its corresponding renderer, TriRenderer. Subsequently, we apply latent diffusion on the Triplane representation to generate high-quality GS objects.
+
+Gaussian splatting uses multi-channel point cloud of "splats" to describe the 3D contents. With a differentiable splats rasterizer, GS has fast rendering speed. However, the sparsity, multiple channels, and uneven distributed density of 3D GS bring great difficulty for 3D generation. We propose to encode GS contents as multi-channel triplane representations, which have been shown to possess favorable properties for representing 3D geometry or NeRF, as demonstrated in previous works Shue et al. [40], Wu et al. [47]. In our work, we leverage the triplane representation to encode both the geometry information and other GS attributes in two separate groups of channels. By training on a dataset of 3D objects, we obtain a shared TriRenderer that is capable of decoding different triplane representations to GS and then render it to image. TriRenderer is fully differentiable, enabling the use of only 2D rendering loss to supervise both the texture and geometry of 3D GS. The advantage of using Triplane to represent GS are two folds. First, it leads to high memory efficiency compared with dense voxels and is expressive enough for generating various 3D GS. Second, Triplane is more compatible with the convolution-based encoders compared with the original sparse GS point cloud, which require specifically designed networks on processing sparse point clouds.
+
+We follow stable diffusion [36] to train DirectTriGS on the proposed triplane representation. Specifically, a VAE is designed to further convert the Triplanes into latent code. We use two separate decoders to decouple the decoding of geometry and GS attributes. Second, we roll out the triplane latent to an expanded multi-channel image, then exploit staged latent diffusion to do generation. Two-stage diffusion is employed to generate the geometry and the corresponding GS appearance. Finally, score distillation sampling (SDS) [35] is adopted as a optional post-processing to refine or restyle the generated 3D objects.
+
+Our contribution can summarize as follows. 1) We propose a Triplane representation for direct 3D GS generation, which is memory efficient to derive GS point clouds with vivid rendering. 2) We design a fully differentiable TriRenderer to enable the end-to-end training of triplane representations, with only 2D supervisions. 3) We develop a Triplane-based GS generation framework DirectTriGS that incorporates a specially designed VAE, latent diffusion module, and a SDS based refiner. 4) Experiments demonstrate our method produces competitive performance in both 3D geometry and multi-view rendering quality in text-to-3D tasks.
+
+# 2. Related Works
+
+3D Object Generation. 1) Multi-view images-to-3D. The first route generates multi-view colored 3D image and then reconstruct the 3D shape and project image to texture, or use score distillation sampling to build 3D object from images produced by 2D diffusion, such as [6, 13, 27, 35, 39, 41]. Since these approaches are actually 2D generator, it is difficult to maintain 3D consistency, which may lead to Janus problem. 2) Image-to-3D. The second route attempt to retrieve 3D geometry from a single input image, such as [25, 28, 53]. With the certain one image as input, the users may be more concerned with the reconstruction quality. 3)Text-to-3D. The third group mainly operate in 3D, which can be clustered by different 3D representation. For example, [10, 11] are able to generate high-quality 3D textured meshes using differentiable rendering; [34, 46] generate colored pointcloud; [1, 14, 23, 31] generate NeRF volumes; [18, 47] generate SDF volumes.
+
+Remark. The input conditions of these three generation methods are gradually becoming abstract, corresponding to increasing difficulty of the generation task, commonly resulting in a gradual decline in the generation quality.
+
+Gaussian Splatting. Gaussian Splatting [21] exploits multi-channel pointcloud of splats to describe the 3D content, which allows real-time rendering of photorealistic scenes. Recently, there emerges so many research focusing on its reconstruction quality enhancement and algorithm optimization [5, 8, 15, 29, 51]. Another related active area includes 4D dynamic GS modeling [3, 44, 49], scene editing [2, 9] and its applications like SLAM [30, 48].
+
+As for GS generation, some works exploit multi-view image based route such as [6, 41], where the image generator output image from required views to enhance the GS rendering in a recursive manner. Rare works explore the GS generation directly in 3D space, such as [53] generates a point cloud using a Transformer structure with 2D image as input, and build a mapping of image to tri-plane encoding of GS attribute; GaussianCube [52] proposes to use optimal transport to model the 3D GS for text-to-3D generation; [16] combine explicit anchor points with implicit
+
+triplane to directly generate GS points.
+
+# 3. Revisiting Gaussian Splitting
+
+Gaussian Splatting [21] uses a set of Gaussian points to describe a 3D object. The Gaussian points are defined by a full 3D covariance matrix  $\pmb{\Sigma}$  in a world space as  $G(\mathbf{x}) = e^{-\frac{1}{2}\mathbf{x}^T\pmb{\Sigma}^{-1}\mathbf{x}}$ , centered at point (mean)  $\mathbf{p} \in \mathbb{R}^3$ . Each point is with a opacity scalar  $\alpha \in [0,1]$  for blending and a series of Spherical Harmonics (SH) coefficients to correctly capture the view-dependent appearance of the scene. The number of SH coefficients are  $3 \times (n + 1)^2$ , where  $n$  denotes the SH order, and higher  $n$  corresponds to more accurate view-dependent appearance.
+
+During rendering, the Gaussians are project to 2D given a viewing transformation  $\mathbf{W}$ . The covariance is transformed as  $\boldsymbol{\Sigma}^{\prime} = \mathbf{J}\mathbf{W}\boldsymbol{\Sigma}\mathbf{W}^{T}\mathbf{J}^{T}$ , where  $\mathbf{J}$  is the Jacobian of the affine approximation of the projective transformation. To ensure  $\boldsymbol{\Sigma}$  to be semi-positive in the whole training process,  $\boldsymbol{\Sigma}$  can be represented by a Cholesky decomposition as  $\boldsymbol{\Sigma} = \mathbf{R}\mathbf{S}\mathbf{S}^{T}\mathbf{R}^{T}$ , represented by a tuple  $s = (s_{1}, s_{2}, s_{3})$  for scaling and a unnormalized quaternion  $\mathbf{q} \in \mathbb{R}^{4}$  for rotation. In summary, each Gaussian point are a union set of position  $\mathbf{p}$  and its GS attributes:
+
+$$
+\mathcal {G} _ {\mathbf {p}} := \{s, \mathbf {q}, \mathrm {S H}, \alpha \}. \tag {1}
+$$
+
+GS pointcloud can be efficiently rendered by a rasterization-based splatting renderer [21], which is fully differentiable.
+
+# 4. Methodology
+
+Our motivation is to directly generate 3D GS with fast speed by utilizing the proposed triplane-based GS representation. While 2D-lifting methods like SDS-based approaches yield intricate results, they are time-intensive and susceptible to Janus problem. Direct generation, notably with fast sampling, can complete 3D generation in under a minute, contrasting with SDS methods that take over 10 minutes or longer, such as [4][43], posing challenges for users. Therefore, direct 3D generation is more practical, with 2D-lifting reserved for enhancing texture details when needed.
+
+The procedures of our generation framework can be divide into 4 stages as shown in Fig.1 (a). Firstly, we encode the 3D objects into triplanes using the TriRenderer. The triplane encoding and TriRenderer training can be concurrently executed with only the multi-view RGBA image and camera poses as supervision. Secondly, a VAE is trained to compress the triplanes to latent space, enabling effective capture of high-level information for subsequent modules. Thirdly, a diffusion model is trained on the triplane latent code. During inference, the diffusion model produces the latent code, which can be decoded back to its corresponding triplane by the VAE decoder. Subsequently, the TriRenderer decodes the triplane into the standard GS point
+
+![](images/0f6b3129f9dafeb1ea97a8c07c5e1e6f91700926f675d7de8e63579c4810257d.jpg)  
+(a) The overall procedure of our 3D content generation framework.
+
+![](images/e89ee7f07caa7332f781434de1779f2cd6006aa281d39e6a1c03fab792483ba9.jpg)
+
+![](images/ac0245851813463f977695cdcb7376eb06ba9d71159ac02010405b1d656ef03f.jpg)
+
+![](images/698df0cca85d4e2868585e5d2158dea4c7d18ef59fe1938a7f12036db508cf97.jpg)
+
+Figure 1. The overview of the proposed 3D GS generation framework and the core component TriRenderer. We use triplane to represent 3D objects, and design a TriRenderer to decode triplane to GS pointcloud and render multi-view images.  
+![](images/a8f4465db2ff41f986e7112ab90158b5fd05a67645196976b27a8d94f6dc0e1c.jpg)  
+(b) The forward pass of the TriRenderer pipeline: rendering a Triolane to multi-view images.
+
+cloud. Finally, an SDS-based refiner can be utilized as an optional post-processing step to enhance or restyle the generated 3D object. Leveraging the pretrained 2D diffusion model within the SDS, the generated GS can be further improved to achieve a more detailed appearance.
+
+# 4.1. Triplane-based GS Field
+
+We employ triplanes to convert the discrete multi-channel GS points into a continuous field, tailored for more efficient encoding in the subsequent generative model. Triplanes are 3 planes formed by every 2 axes of  $x,y,z$  axes in 3D space, where every 3D point  $\mathbf{p}$  can query these planes to get corresponding features  $F_{\mathbf{p}} = (F_{xy},F_{xz},F_{yz})$  using orthogonal projection. In real implementation, triplane is a tensor with the size of  $3\times H\times H\times C$ , where  $H$  denote the resolution along every axis and  $C$  is the feature channel. The query of point with arbitrary continuous coordinate should be a bi-linear interpolation in the triplane grids. Considering GS is a set of points with multiple channels of attributes, it is natural to use triplane for GS encoding. If the triplane feature and GS attributes of a point can be transformed to each other, the sparse GS pointcloud of every object can be represented as continuous triplane GS field for further encoding. We use separate channels to encode 3D geometry and other GS attributes as described in Eq. 1, which is an experimental setting for better convergence in the training.
+
+# 4.2. TriRenderer
+
+The TriRenderer serves as the crucial component for converting a 3D object into a triplane-based GS field. It acts as a fully differentiable bridge connecting the GS field with
+
+rendering, enabling the optimization from 2D images to geometry and appearance encoding.
+
+As depicted in Fig. 1 (b), the TriRenderer comprises a geometry branch and a GS attribute branch, each equipped with independent decoders to decode the triplane. The geometry branch is responsible for retrieve the geometry as triangular mesh from triplane, with a surface sampler for GS pointcloud sampling. Then GS attribute branch uses the obtained pointcloud to query the triplane to obtain the GS attribute corresponding to each point. In this way, the GS pointcloud in the original format is retrieved, and can be rendered using the original GS renderer. It is worth mentioning that all triplanes of different object share a common TriRenderer, which ensures the features on different triplanes subject to a similar distribution.
+
+Geometry Branch. We use signed distance function (SDF) to represent the geometry, and allow every vertex deform as [37], so that the geometry branch decodes  $F_{p}$  to a SDF volume and its vertex deformation. By query all grid coordinates of the designated resolution  $L \times L \times L$ , the deformable SDF volume is reconstructed. Then we exploit a differentiable Marching Cube algorithm FlexiCubes [38] to extract triangular mesh from the SDF volume.
+
+Surface Sampling. Considering that GS pointcloud is generally gathered on the surface of objects, we randomly sample GS points on the faces of triangular mesh with barycentric coordinates. We expect that every splat is flat and with a normal consistent with its source triangular face. Assume a face is formed by vertices  $< v_{a}, v_{b}, v_{c} >$ , and vector  $\mathbf{v}_{1} = (v_{a} - v_{b})$ ,  $\mathbf{v}_{2} = (v_{b} - v_{c})$ , the face normal can be calculated as  $\mathbf{n} = \mathbf{v}_{1} \times \mathbf{v}_{2}$ . Then the rotation matrix of every
+
+splat drawn from this face can be formulated as
+
+$$
+\mathbf {R} = \left[ \mathbf {v} _ {1}, \mathbf {n} \times \mathbf {v} _ {1}, \mathbf {n} \right], \tag {2}
+$$
+
+which can be transform to  $\mathbf{q}$  in Eq.1 by standard matrix-to-quaternion algorithm. To make the splats flat,  $s_3$  in Eq.1 is fixed to an infinite small value.
+
+To further reduce the computational load in the subsequent GS rendering process, only faces oriented toward the camera are sampled. These face indices can be obtained through fast rasterization of the mesh faces. Note this rasterization is not required to be differentiable, and we use the library Nvdiffrast [22] for implementation.
+
+GS Attribute Branch. By querying the triplane GS channels with the sampled pointcloud, we can obtain the GS feature and use the GS attribute branch to transform them to the rest GS attributes. Then the GS renderer can render GS pointcloud to multi-view images. Since different GS attributes have different numerical scales and distributions, we customize individual headers to decode them respectively, which is similar to [53].
+
+Training. The training consists of 2 stages. In the first stage, a small batch of data is used to train the triplanes and the TriRenderer together. The second stage involves the whole dataset to train all triplanes with the parameters of TriRenderer frozen. In this way, we can handle large dataset by distributed training in the second stage, and the same TriRenderer can be shared by all triplanes. There is no need to pre-train the GS pointcloud using original GS training as [21].
+
+The only required supervision data is  $N$  multi-view images  $\{I_i\}_{i=1}^N$  with camera poses, and the training losses consist of the rendering loss  $L_{\mathrm{render}}$  and the geometric regularization  $L_{\mathrm{geo}}$ . The rendering loss is a weighted sum as
+
+$$
+L _ {\text {r e n d e r}} = w _ {1} L _ {\text {a l p h a}} + w _ {2} L _ {\text {r g b}} + w _ {3} L _ {\text {p i p s}}, \tag {3}
+$$
+
+where  $L_{\mathrm{alpha}}$  is a  $L_{1}$  loss on the alpha map, namely the silhouette image loss;  $L_{\mathrm{rgb}}$  is a combination of  $L_{1}$  pixel loss and SSIM loss [42] between rendered image  $\hat{I}_i$  and ground truth  $I_i$ :
+
+$$
+L _ {\mathrm {r g b}} = \sum_ {i = 1} ^ {N} (1 - \beta) \| I _ {i} - \hat {I} _ {i} \| _ {1} + \beta \operatorname {S S I M} \left(I _ {i}, \hat {I} _ {i}\right), \tag {4}
+$$
+
+and  $L_{\mathrm{pips}}$  is the perceptual loss [17].  $w_{1}, w_{2}, w_{3}$  and  $\beta$  are all weighting factors determined by experiments.
+
+The geometric regularization loss on the SDF volume  $V$  is defined as
+
+$$
+L _ {\text {g e o}} = \gamma_ {1} L _ {\text {d e v}} + \gamma_ {2} L _ {\text {w e i g h t i n g}} + \gamma_ {3} L _ {\text {C E}} + \gamma_ {4} L _ {\text {s i g n}}, \tag {5}
+$$
+
+where the  $L_{\mathrm{dev}}$  and  $L_{\mathrm{weighting}}$  are defined by Flex-cubes [38] to regularize the extracted connectivity and the weighting scale of SDF vertices. To penalize the sign
+
+changes on all grid edges, we follow [33] to define  $L_{\mathrm{CE}}$  as
+
+$$
+L _ {\mathrm {C E}} = \sum_ {(s _ {a}, s _ {b}) \in \epsilon} \operatorname {C E} \left(\sigma \left(s _ {a}\right), \operatorname {s i g n} \left(s _ {b}\right)\right), \tag {6}
+$$
+
+where CE denotes cross entropy;  $\epsilon$  is the set of all edges connecting vertices with different signs; and  $\sigma$  is the sigmoid function. Finally,  $L_{\mathrm{sign}}$  is designed to prevent the SDF volume from being trapped in an empty shape, i.e. a fully positive or fully negative SDF volume,
+
+$$
+L _ {\text {s i g n}} = \delta (V) M (| V |), \tag {7}
+$$
+
+where  $\delta (V) = 1$  if  $V$  is empty, otherwise  $\delta (V) = 0$ .  $M(|V|)$  denotes the mean of the absolute value of  $V$ .
+
+# 4.3. Triplane VAE
+
+We employ an UNet-like structure of VAE to compress the triplane to latent space. The training pipeline is demonstrated in Fig. 2 (a). Considering that the 3 planes of triplanes encodes features from 3 orthogonal view direction, these 3 planes should be homogeneous data, so that We reshape the triplanes of batchsize  $B$  to a new batch as  $B \times 3 \times H \times H \times C$  to  $3B \times H \times H \times C$  for the VAE training. We use decoupled encoders and decoders for geometry and GS channels of triplanes, for experiments prove that a mixed encoding may lead to blur of the rendering results. After the triplane is reconstructed, the TriRenderer trained in Section.4.1 can be used to retrieve the GS pointclouds and render it to images.
+
+In the training process, same loss functions as Eq. 3 and Eq. 5 are used, along with an  $L_{1}$  loss between the input and reconstructed triplanes, denoted as  $L_{\mathrm{Tri}}$ . Additionally, a Kullback-Leibler divergence loss  $L_{\mathrm{KL}}$  is included to ensure that the latent variables do not deviate significantly from a normal distribution. The total losses is summarized as
+
+$$
+L _ {\mathrm {V A E}} = L _ {\mathrm {T r i}} + L _ {\mathrm {G e o}} + L _ {\mathrm {R e n d e r}} + \gamma L _ {\mathrm {K L}}, \tag {8}
+$$
+
+where  $\gamma$  is a small weight.
+
+# 4.4. Two-stage LDM for Text-to-3D Generation
+
+Taking into account the significant relevance of texture appearance to the underlying geometry, we proposed to utilize staged diffusion to generate geometry and GS attribute successively as shown in Fig. 2 (b). It is easy to implement it because the latent codes for geometry and other GS attributes are totally decoupled by VAE, as mentioned earlier. In this way, the geometry code can be a new condition for the second stage.
+
+We follow DDPM [12, 20] to implement the text-conditioned LDM. To better capture the relation between different planes, we roll out the triplane latent of  $B \times 3 \times h \times h \times c$  to a image-like  $B \times 3h \times h \times c$  as the input of diffusion model, and the generated result will be transformed back to the original shape for TriRenderer decoding.
+
+![](images/d4d455d7b936a86017daee34945deaf08686bcf6beb9a8f6ab8da1af198305b4.jpg)  
+Figure 2. Triplane VAE and 2-stage diffusion.
+
+# 4.5. SDS-based Texture Booster
+
+To refine or restyle the generated GS pointcloud, we utilize a pretrained 2D diffusion model for the SDS training process [35] as shown in Fig. 3. As the generated 3D GS is constrained by the mesh reconstructed from SDF, detailed in Section 4.2, we maintain the GS splats' adherence as previously established. However, we enable the mesh vertices to shift within a limited radius to enhance the stability of the SDS process. Additionally, throughout the entire SDS procedure, there is no need for densification or pruning operations. This ensures that the number of points can be controlled to align with the number of mesh faces.
+
+With the image rendered from the initial GS pointcloud, the 2D diffusion model can produce images with better 2D/3D consistence in different views, so that the optimization process can converge rapidly without Janus problem.
+
+# 5. Experiment
+
+The experiments are conducted step-by-step according to the generation pipeline proposed as Fig.1 (a). We use OmniObject3D [45] dataset for toy experiments, and Objiverse [7] dataset for main evaluation. First, we sample 200K object to train their co顺应ing triplanes and TriNDERer. Then we train the VAE and diffusion model for 3DS GS generation. Finally, we exploit SDS to boost the texture quality for unsatisfactory generated objects. The procedure of data pre-processing and the implementation details are included in the supplementary materials.
+
+The experimental results primarily consist of the following components: 1) For examining the proposed triplane modeling for GS generation, we focus on the text-to-3D task and showcase the direct GS generation outcomes qualitatively and quantitatively. These results are compared with Shap-E [19], Direct3D [26], and the most recent Gaussian-Cube [52]. 2) In comparison to 2D-lifting GS generation methods, we present the performance of SDS refinement on unsatisfying samples, with GsGEN [4] and GaussianDreamer [50] as baselines.
+
+# 5.1. Triplane Fitting and VAE Reconstruction
+
+Triplane Fitting. We adopt a resolution of  $3 \times 128 \times 128 \times 16$  for all triplane fitting, with a resolution of  $64 \times 64 \times 64$  for the deformable SDF grids. We randomly sample 1000 objects for the shared TriRenderer training, and train all residual objects distributively. Every triplane is initialized with Gaussian noise before training. Under such settings, every triplane takes less than 30 seconds for geometry and GS appearance reconstruction.
+
+VAE Reconstruction. We use a down-sample factor of 4 to compress the triplanes to latent space.
+
+We visualize the triplane and the VAE reconstruction results of several data samples for a simple check, please refer to the supplementary materials.
+
+# 5.2. Direct Text-to-3D GS Generation by LDM
+
+In this section, we present the results of our 3D GS object generation without the SDS refinement, both quantitatively and qualitatively. Due to the current scarcity of work targeting direct 3DGS generation, we selected two state-of-the-art text-to-3D works based on other 3D representations(NeRF) Shap-E [19] and Direct3D [26] for comparison. For fairness, these selected methods also perform direct generation in the 3D domain without any 2D prior knowledge or refinement based on 2D diffusion. Additionally, for the limited space, we provide more generation results and comparison with other methods such as GaussianCube [52] in the supplementary materials.
+
+Qualitative Results. The generation results from different methods are listed in Fig. 4. Every generated sample is rendered from different views accompanied by the provided text prompt captioned beneath the images. Our method showcase enhanced proficiency in both geometry and rendering quality, resulting in sharper and clearer outputs, which can be further verified in the subsequent quantitative evaluation. For more generated samples, please check the supplementary materials.
+
+Quantitative Results. We use CLIP score to evaluate the text-to-3d consistency, and an user study is conducted to evaluate the generation results from various aspect such as geometry, texture, realistic rendering and the consistency
+
+![](images/1c5fae7808bcece9143adcb3cb11fbe33f733882894530679f672ec3c79ce3e9.jpg)  
+Figure 3. Score distillation process(SDS) for optional texture refinement.
+
+<table><tr><td></td><td>Geometry↑</td><td>Texture↑</td><td>Realism↑</td><td>Consistency↑</td><td>Overall↑</td></tr><tr><td>Shap-E</td><td>3.080</td><td>3.019</td><td>2.947</td><td>3.121</td><td>3.042</td></tr><tr><td>Direct3D</td><td>3.222</td><td>3.150</td><td>3.118</td><td>3.242</td><td>3.183</td></tr><tr><td>Ours</td><td>3.456</td><td>3.383</td><td>3.332</td><td>3.520</td><td>3.423</td></tr></table>
+
+Table 1. User study on generated 3D objects (Our results are raw outputs from LDM without SDS refinement).  
+
+<table><tr><td></td><td>Shap-E</td><td>Direct3D</td><td>Ours</td></tr><tr><td>openai:ViT-L-14</td><td>0.2398</td><td>0.2152</td><td>0.2456</td></tr><tr><td>openai:ViT-L-14-336</td><td>0.2426</td><td>0.2220</td><td>0.2462</td></tr></table>
+
+Table 2. CLIP score(↑) for evaluation of similarity between rendered images and given text prompt((Our results are raw outputs from LDM without SDS refinement)).  
+
+<table><tr><td></td><td>More Realistic (%)</td><td>More Detailed (%)</td><td>Overall (%)</td></tr><tr><td>GaussianDreamer</td><td>35.0</td><td>50.0</td><td>42.5</td></tr><tr><td>GSGEN</td><td>17.5</td><td>5.0</td><td>11.3</td></tr><tr><td>Ours</td><td>47.5</td><td>45.0</td><td>46.3</td></tr></table>
+
+with given prompt. 49 users participated in the user study to score the over 50 3D samples from 1 to 5 points, and the average results are shown in Tab. 1. As for the CLIP score, the open-source repository t2vmetrics [24] is used to calculate the CLIP score on two versions of ViT models, and the results are demonstrated in Tab. 2. Both the CLIP score and the user study indicate that the proposed method produces better performance.
+
+# 5.3. Optional Texture Boosting by SDS
+
+To compare with other SDS-based 3D GS generation methods, we implement a version of SDS for our mesh-binding GS representation as described in Section 4.5. GsGEN [4] and GaussianDreamer [50] are selected as our baselines. The generated samples, as illustrated in Fig. 5, highlight that with the SDS refiner, our DirectTriGS can deliver competitive outcomes comparable to the state-of-the-art 2D-lifting methods.
+
+Furthermore, we conducted a user study for quantitative evaluation. 40 users were tasked with ranking 15 samples from different methods based on two criteria: realism and level of detail. The results indicate that our approach marginally outperforms the other baseline methods.
+
+Table 3. User study on generated 3D objects (with SDS).  
+
+<table><tr><td></td><td>TFLOPs</td><td>Paras.(M)</td><td>GPU Mem.(GB)</td><td>Running Time (Sec.)</td></tr><tr><td>Generation</td><td>0.00823</td><td>56.65</td><td>2.94</td><td>16.2</td></tr></table>
+
+Table 4. Generation inference efficiency, with the batch size is 1.
+
+# 5.4. Ablation Study
+
+3D Diffusion for voxel-based Gaussian Splitting. We attempt to do GS attribute generation conditioned on given voxel occupancy via 3D diffusion model. However, even a toy experiment of over-fitting one single object failed, which may attributes to the complex multiple channels with different distributions especially the non-Euclidean ones such as quaternion. As shown in Fig.6, the diffusion model learns to generate color but fails to generate splat scaling, opacity and orientation.
+
+Triplane Diffusion without VAE. Since VAE inherently involves a reconstruction loss, we attempt to use direct diffusion on the triplane space for generation. The experiment results show that such direct diffusion may cause serious noise on decoded geometry. Randomly generated samples are visualized in Fig.7. A possible reason is that the multichannels of triplane contain considerable noisy redundancy, which is difficult for the LDM to filter.
+
+Inference Efficiency. The inference efficiency is listed in Table 4. This experiment is conducted on the platform equipped with RTX3090 GPU with 24GB memory.
+
+# 6. Conclusion & Acknowledgment
+
+We have presented a novel framework DirectTriGS for Gaussian Splatting Field generation. DirectTriGS mainly consists of 3 parts: 1) a light-weight triplane representation for 3D object with the format of Gaussian Splatting; 2) a fully differentiable TriRenderer which can decode triplane to original GS and render it to multi-view images; 3) the triplane VAE and staged diffusion model for the whole generation process. By utilizing our DirectTriGS, the intricate GS data can be generated directly and efficiently. 4) Additionally, we incorporate a SDS refiner to further improve the texture and details of generated objects.
+
+This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by NSFC-RGC Joint Fund Project N_CUHK498/24. Hongsheng Li is a PI of CPII under the InnoHK.
+
+![](images/e02b0b9e340b51003f4a0af94ca505b938ab38185310a1aeae72930ffb0077bf.jpg)
+
+![](images/a8d52a97ba35677a7fd3927da59bc8ef5a17462e5f80d1462158dcac99b07aee.jpg)
+
+![](images/c451f8c67b51d102c44bd5f968217768c2cc62129beff2a09320df123d8df510.jpg)
+
+![](images/ecdf04e07c1cb4999e734e4316aba7b2d96e2e51b03be480578dcba990b57259.jpg)
+
+![](images/2ceb55e32e7787145e7f5b7b418411f8833e84c28a3f12e7ba41dfae5427d41f.jpg)
+
+![](images/c93a0fea47463fb7388dd9b94157b2696942a779c3ac022e0750f2e3979a18f9.jpg)
+
+![](images/939ef3c413b258a30bc7602ce90f5916e697e334b760bbc40b742c461fa27860.jpg)
+
+![](images/0db8dc473bcd8b9a0ec8866a96e32cf4eb5c73d79cb8f8e5cc1486d0b098f5af.jpg)  
+(a) Comparison with Direct3D.
+
+![](images/3bbb6ee05be3c129040b8c07a2869f056326c0048e52df83b029f2edbef790fa.jpg)
+
+![](images/7e68078254c1997822946878565641ef1c291448b2668b07fbb52580f39748ae.jpg)
+
+![](images/9a8f5f4e995cc14f49033c609e54d995cee059d85cbd38496bf0708bf7e03383.jpg)
+
+![](images/67d5c93c197f13c32b1ede71b73b93751838c6c0d5ccf21da19b76caa3ce5c98.jpg)
+
+![](images/ef41a3cd14b7ec0b934bd4833be2c8df5f63f92d873c950331dddcc120b9a90e.jpg)
+
+![](images/1c07367dad90481bf51654c2997d2915314471b3926331b615d5c02e577bc444.jpg)  
+(b) Comparison with Shap-E.
+
+![](images/64b850aa9cfd764ef1cd388e358115550c22469c903a819a75a3b9afb6f2b7ee.jpg)  
+Figure 4. Comparison of generated 3D objects (Raw results without any refinement such as SDS).
+
+![](images/f4e11a8500518460496587dd8c168e83c9614b6ac6d4ada9d2df5d5f61050a85.jpg)  
+Figure 5. Refinement of unsatisfactory results by SDS, compared with pure SDS-based methods GsGEN and GaussianDreamer.
+
+![](images/98d34b585d9c24f1d501d70cd8477cd25c8c9773309fff17b241ddca3c0e9f35.jpg)  
+Figure 6. Failure of GS attribute generation.
+
+![](images/95a0e5c3a1fbb9d463967d6d26657d1dad5d10e760be06d36e579c5a787388b9.jpg)  
+Figure 7. Noisy results of direct diffusion on triplane. The condition prompt are "train", "watermelon" and "box".
+
+# References
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+        "type": "text",
+        "text": "Directional Label Diffusion Model for Learning from Noisy Labels",
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+        "text": "Senyu Hou $^{1}$ , Gaoxia Jiang $^{1}$ , Jia Zhang $^{1}$ , Shangrong Yang $^{1}$ , Husheng Guo $^{1}$ , Yaqing Guo $^{1}$ , Wenjian Wang $^{2*}$",
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+        "text": "$^{1}$ School of Computer and Information Technology, Shanxi University, China  \n $^{2}$ Key Laboratory of Computational Intelligence and Chinese Information Processing Ministry of Education, Shanxi University, China",
+        "bbox": [
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+        "text": "{202312407005, 202412407035}@email.sxu.edu.cn",
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+        "type": "text",
+        "text": "{jianggaoxia, sryang, guohusheng, yqguo, wjwang}@sxu.edu.cn",
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+    {
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+        "text": "Abstract",
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+        "text": "In image classification, the label quality of training data critically influences model generalization, especially for deep neural networks (DNNs). Traditionally, learning from noisy labels (LNL) can improve the generalization of DNNs through complex architectures or a series of robust techniques, but its performance improvement is limited by the discriminative paradigm. Unlike traditional ways, we resolve the LNL problems from the perspective of robust label generation, based on diffusion models within the generative paradigm. To expand the diffusion model into a robust classifier that explicitly accommodates more noise knowledge, we propose a Directional Label Diffusion (DLD) model. It disentangles the diffusion process into two paths, i.e., directional diffusion and random diffusion. Specifically, directional diffusion simulates the corruption of true labels into a directed noise distribution, prioritizing the removal of likely noise, whereas random diffusion introduces inherent randomness to support label recovery. This architecture enable DLD to gradually infer labels from an initial random state, interpretably diverging from the specified noise distribution. To adapt the model to diverse noisy environments, we design a low-cost label precorrection method that automatically supplies more accurate label information to the diffusion model, without requiring manual intervention or additional iterations. Our approach outperforms state-of-the-art methods on both simulated and real-world noisy datasets. Code is available at https://github.com/SenyuHou/DLD.",
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+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Deep neural networks (DNNs) have achieved notable success across key areas of machine learning, driven by the growth of datasets and the increase in model parameters.",
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+        "text": "These models are primarily trained using supervised learning, which relies heavily on large volumes of labeled data [5]. However, real-world data often suffer from low-quality labels due to subjective errors like indistinguishable samples or objective errors such as incorrect label recording, making noisy labels a widespread issue [13, 55]. Studies have shown that the generalization capability of deep neural networks is adversely affected when trained with noisy labels [1, 59]. Consequently, it is crucial to develop methods for learning from noisy labels (LNL) on large-scale but low-quality datasets.",
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+        "text": "Due to the varied distribution of label noise, historical research has classified it into class-conditional noise (CCN) and instance-dependent noise (IDN) [57]. Recent studies indicate that label noise in real datasets predominantly aligns with the IDN assumption, wherein noise is unevenly distributed and more likely in samples with similar features [2, 6, 10–12, 51]. To tackle these complex noise patterns, mainstream LNL methods employ strategies combining filtering and training approaches. Some studies demonstrate a phenomenon known as the memorization effect [1, 3, 29, 56], i.e., DNNs first learn from simple data before fitting to noisy samples. Based on this observation, sample selection strategies utilize confidence levels or prediction loss during training intervals to identify noisy samples [17, 24, 28, 58]. However, this strategy is inherently risky, as the timing of noise memorization varies across datasets and noise distributions, complicating the selection criteria [6, 39]. Consequently, mainline LNL methods can often be integrated with training strategies to enhance model robustness, employing techniques like label filtering [17, 36, 50, 58], label correction [47, 60, 64], robust loss [16, 48, 61], and semi-supervised learning [28]. Among these techniques, semi-supervised learning, by combining multiple approaches [34, 37, 49], often outperforms other LNL methods but is still constrained by the discriminative framework. Although some researches attempt to combine",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "type": "page_footnote",
+        "text": "*Corresponding author.",
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+    {
+        "type": "page_number",
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+    {
+        "type": "text",
+        "text": "variational autoencoders (VAE) [25] with DivideMix [28] to address label noise [15], most methods remain focused on discriminative models.",
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+        "text": "In this paper, we shift away from the traditional LNL perspective, proposing robust classification models using label diffusion models that focus on the generative modeling and deeply explores the generative relationship between features and labels. Under this paradigm, labels are generated by gradually refining an initial random guess. The uncertainty modeling in diffusion models inherently meets some robustness requirements, as random label generation can offset some noise interference [4, 18]. However, this type of diffusion process lacks information about noisy labels. Intrinsic uncertainty alone is insufficient to handle complex noisy environments. Inspired by the residual diffusion denoising models (RDDM) [32], we explore a novel Directional Label Diffusion (DLD) model that incorporates noisy label information into the diffusion process. In DLD, we decouple the diffusion process into two channels: directional diffusion and random diffusion (see Figure 1). The directional diffusion guides the initial label towards a more probable noise direction (e.g., a green automobile may be misclassified as a frog or other classes, as indicated by the probability distribution in the third column in Figure 1), while random diffusion retains the original diffusion mechanism. This approach injects information about which categories should not be generated into the label generation paradigm, enhancing the interpretability of the diffusion model's robust inference. Unlike conventional label diffusion, our diffusion process concludes with an endpoint that includes the potential noise distribution of the sample (i.e.,  $\\mathbf{y}_T = \\mathbf{y}_n + \\epsilon$ ) and employs two independent coefficient schedules to control the diffusion speed of both channels.",
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+        "type": "text",
+        "text": "One challenge is that only noisy labels are available in practice for training, so neither  $\\mathbf{y}_0$  nor  $\\mathbf{y}_n$  can be obtained directly. Few researchers employed neighborhood detection techniques like KNN to re-estimate  $\\mathbf{y}_0$  [4]. However, under the IDN assumption, neighborhood labels of noisy samples often contain similar errors, making naive label estimation methods unreliable and potentially causing  $\\mathbf{y}_0$  to deviate from the ground truth (see Figure 3). To address these issues, we further propose a straightforward and efficient label pre-correction method that automatically provides diverse label information for diffusion model training. This framework employs feature extractors to identify the neighborhood label distribution of samples. Note that these extractors are either trained with self-supervised methods [7, 19, 65], which require few additional training iterations, or use pre-trained models without further training, thus remaining unaffected by label noise. Additionally, this pre-correction strategy allows the seamless integration of pre-trained large-scale models such as Sim-CLR [7] and vision transformer (ViT) [40] into our framework to further",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "boost the performance. The main contributions of this work are summarized as follows:",
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+        "type": "list",
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+        "list_items": [
+            "- We propose a novel Directional Label Diffusion (DLD) model that explicitly introduces interpretable noise information through a dual diffusion architecture, enabling robust learning of label generation patterns from noisy data.",
+            "- We design a fast label pre-correction method that automatically provides more accurate label information for the diffusion process and richer feature conditions for the generation process. By leveraging the consistency principle, this method pre-estimates the label distribution in a single iteration without incurring additional costs.",
+            "- We refine the paradigm for introducing feature conditions with rigorous theoretical deduction and provide complementary training strategies to enhance robustness further.",
+            "- We experimentally show that our model surpasses the state-of-the-art (SOTA) methods on both simulated and real-world noisy datasets, e.g.,  $6\\% \\sim 21\\%$  accuracy improvement on the CIFAR-100 dataset with IDN."
+        ],
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Learning from Noisy Labels",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Screening and training strategies are central to LNL methods, aiming to distinguish noisy from clean samples and to optimize model learning under noisy conditions. Screening strategies, like Co-teaching [17], select low-loss samples as clean, while DivideMix [28] uses a Gaussian mixture model to automatically identify clean samples during training. Confidence-based methods like CC [62] and DISC [31] classify samples with unreliable predictions as noisy, whereas neighbor consistency regularization (NCR) [22] promotes learning from samples with high neighbor consistency. Our pre-correction method is based on similarity constraints across multi-view label distributions and leverages a feature extractor to provide high-quality information to the diffusion model without requiring additional iterative training. For training, models such as SEAL [6] iteratively correct noisy labels, but this often risks worsening outcomes [23]. Robust loss functions, like mean absolute error (MAE) [16] and generalized cross entropy (GCE) [61], enhance resilience to noisy labels, while DAC [45] and DMI [54] offer advanced mutual information-based losses. Approaches like DivideMix [28] treat LNL as semi-supervised learning, supported by methods like CC [62], C2D [63], and ELR [33] to refine the process. Without complex iterations or loss design, our method utilizes a lightweight diffusion network and a simple L2 loss to quickly learn the feature-label generation relationship.",
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+    },
+    {
+        "type": "text",
+        "text": "2.2. Label Denoising Diffusion Models",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Diffusion models were initially designed for image generation tasks and can be understood through the lenses of score matching and dynamics. Ho et al. [21] introduced a",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "25739",
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+    {
+        "type": "image",
+        "img_path": "images/c07b814ed34be5d0f57d0b65e23ec6f71e12a29dad6bf275b3b5b1a6c5210b02.jpg",
+        "image_caption": [
+            "Figure 1. The proposed Directional Label Diffusion (DLD) model includes diagrams illustrating both the forward and reverse processes. In the forward process, diffusion is decoupled into two channels: random diffusion and directional diffusion. Random diffusion represents the transformation of  $\\mathbf{y}_0$  into random Gaussian noise  $\\epsilon$ , while directional diffusion describes the transformation of  $\\mathbf{y}_0$  into a specific sample noise label distribution  $\\mathbf{y}_n$ . Ultimately,  $\\mathbf{y}_0$  diffuses to the endpoint  $\\mathbf{y}_T = \\mathbf{y}_0 + \\epsilon$ . Notably, the features of the samples serve as control conditions, guiding the generation of labels only during the reverse process."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "more classical interpretative framework known as denoising diffusion probabilistic models (DDPM), which have been widely applied across diverse domains. RDDM expands the denoising-based diffusion models, initially uninterpretable for image restoration, into a unified and interpretable model for both image generation and restoration by introducing residuals. Classification and regression diffusion models (CARD) [18] reconstruct the classification as a conditional generative task, generating labels from dimensionally reduced image features via a pre-trained encoder. Building on CARD, label-retrieval-augmented (LRA) diffusion model [4] re-estimates the generation targets through neighbor label retrieval, improving label accuracy. Our model disentangles the diffusion process into directional and random diffusion channels, enhancing diffusion quality through precorrection, which leads to train a more robust label diffusion model.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Preliminary",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we primarily introduce the label denoising diffusion models (LDDM), which is constructed based on the theoretical framework of the DDPM [21]. We start by defining the data distribution  $\\mathbf{y}_0\\sim q(\\mathbf{y}_0)$  and a Markovian forward (diffusion) process  $q$  , which progressively adds Gaussian noise  $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$  to the labels based on diffusion strength  $\\beta_{t}$  , diffusing label  $\\mathbf{y}_0$  to  $\\mathbf{y}_T$  ..",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(\\mathbf {y} _ {t} \\mid \\mathbf {y} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {y} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {y} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Under Bayes' theorem, one finds that the posterior distribution of the forward process can be represented as a Gaussian distribution with mean  $\\tilde{\\mu}_t(\\mathbf{y}_t,\\mathbf{y}_0)$  and variance  $\\tilde{\\beta}_t$  :",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(\\mathbf {y} _ {t - 1} \\mid \\mathbf {y} _ {t}, \\mathbf {y} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {y} _ {t - 1}; \\tilde {\\mu} _ {t} \\left(\\mathbf {y} _ {t}, \\mathbf {y} _ {0}\\right), \\tilde {\\beta} _ {t} \\mathbf {I}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tilde{\\mu}_t(\\mathbf{y}_t,\\mathbf{y}_0) = \\frac{\\sqrt{\\bar{\\alpha}_{t - 1}}\\beta_t}{1 - \\bar{\\alpha}_t}\\mathbf{y}_0 + \\frac{\\sqrt{\\alpha_t(1 - \\bar{\\alpha}_{t - 1})}}{1 - \\bar{\\alpha}_t}\\mathbf{y}_t$  and  $\\tilde{\\beta}_t = \\frac{1 - \\bar{\\alpha}_{t - 1}}{1 - \\bar{\\alpha}_t}\\beta_t$ , In the reverse process, we naturally employ a neural network to perform Markovian inference from  $q(\\mathbf{y}_T)$ , fitting the posterior distribution  $q(\\mathbf{y}_{t - 1}|\\mathbf{y}_t)$  through to  $\\mathbf{y}_0$ . Since the variance of the posterior Gaussian distribution depends only on the diffusion strength corresponding to time  $t$ , the neural network focuses primarily on predicting and learning the mean:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\theta} \\left(\\mathbf {y} _ {t - 1} \\mid \\mathbf {y} _ {t}\\right) := \\mathcal {N} \\left(\\mathbf {y} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {y} _ {t}, t\\right), \\tilde {\\beta} _ {t} \\mathbf {I}\\right). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To train this model such that  $p_{\\theta}(\\mathbf{y}_0)$  closely approximates  $q(\\mathbf{y}_0)$ , we can optimize the variational lower bound (VLB), however, research [7] found that directly predicting the mean was not effective, so they reparameterized the estimation target, constraining the neural network to estimate the actual noise of the diffusion process and simplified the loss function:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {s i m p l e}} := E _ {t \\sim [ 1, T ], \\mathbf {y} _ {0} \\sim q (\\mathbf {y} _ {0}), \\epsilon \\sim \\mathcal {N} (0, \\mathbf {I})} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {y} _ {t}, t) \\| ^ {2} \\right]. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "During inference, we utilize the label noise estimated by the model, restoring the mean of the label at time  $t - 1$  to retrieve its distribution form, and then gradually performing random sampling until generating the label  $\\mathbf{y}_0$ :",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {y} _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {y} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (\\mathbf {y} _ {t}, t)\\right) + \\sqrt {\\tilde {\\beta} _ {t}} \\mathbf {z}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            527,
+            795,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{z} \\sim \\mathcal{N}(0, \\mathbf{I})$ . Unfortunately, this label generation process lacks any conditional information, resulting in random label generation for images with identical features, which fails to achieve classification. To address this, we",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "25740",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "analyze the foundational paradigm of conditional label diffusion models in Appendix A and simplify the method of feature conditioning.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Directional Label Diffusion Model",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Based on LDDM, our goal is to develop a directional diffusion process on labels to introduce more knowledge about noise. We modify the representation of  $\\mathbf{y}_T = \\epsilon$  in LDDM to  $\\mathbf{y}_T = \\mathbf{y}_n + \\epsilon$  in our DLD, where  $\\mathbf{y}_n$  is an estimation of noisy label distribution. The improved forward process is no longer a simple random noise diffusion but is disentangled into two paths of directional diffusion and random diffusion, as shown in Figure 1.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the following subsections, we first outline the overall framework of our model in Section 4.1. Next, in Section 4.2, we present the foundational theory of the DLD diffusion process and analyze the method of conditional control. In Section 4.3, we describe the reverse process and training method, including optimizations for introducing feature conditions and an adapted accelerated inference method. Finally, in Section 4.4, we describe the rapid label pre-correction method within the DLD framework.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Model Overview",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We propose the Directional Label Diffusion (DLD) framework, with the overall process illustrated in Figure 2. The framework contains two main stages: label pre-correction (Stage 1) and the directional label diffusion model (Stage 2). In stage 1, we first use two different data augmentation methods to provide two views for each sample, then use a pre-trained feature extractor  $f_{ext}$  to observe the neighborhood label distribution  $p_w$  and  $p_s$  of the same sample in two feature spaces. Based on similarity constraints and the principle of neighborhood consistency, we divide the dataset into clean, noisy, and hard sets. Then, the label precorrector and noise distribution estimator prepare  $\\mathbf{y}_0$  and  $\\mathbf{y}_n$  based on the sample partitioning results, using  $\\mathbf{y}_0$  as the initial diffusion label and  $\\mathbf{y}_n$  as part of the diffusion endpoint for the next stage of model training. Otherwise, we introduce both augmented image features and high-quality features extracted by  $f_{ext}$  into the training process to jointly guide the learning of the robust diffusion model.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Forward Process of DLD",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To model the random diffusion of labels and the addition of directional noise information, we define the single forward (diffusion) process step in our DLD as follows:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {y} _ {t} = \\mathbf {y} _ {t - 1} + \\alpha_ {t} \\mathbf {y} _ {d} + \\beta_ {t} \\epsilon , \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{y}_d$  is the deviation between  $\\mathbf{y}_n$  and  $y_0$  (i.e.,  $\\mathbf{y}_d = \\mathbf{y}_n - \\mathbf{y}_0$ ), representing the directional shift contained in the diffusion from  $\\mathbf{y}_{t-1}$  to  $\\mathbf{y}_t$ . Two independent coefficients,  $\\alpha_t$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "and  $\\beta_{t}$  control the degrees of directional and random diffusion, respectively. Based on the additivity of Gaussian noise, we derive the jump diffusion formula from  $\\mathbf{y}_0$  to  $\\mathbf{y}_t$  without requiring single-step continuous diffusion (see Appendix B for the proof):",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {y} _ {t} = \\mathbf {y} _ {0} + \\bar {\\alpha} _ {t} \\mathbf {y} _ {d} + \\bar {\\beta} _ {t} \\epsilon , \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\bar{\\alpha}_t = \\sum_{i=1}^t \\alpha_i$  and  $\\bar{\\beta}_t = \\sqrt{\\sum_{i=1}^t \\beta_i^2}$ . When  $t = T$ , we hope  $\\mathbf{y}_T = \\mathbf{y}_n + \\epsilon = \\mathbf{y}_0 + \\mathbf{y}_d + \\epsilon$ , so we usually set  $\\bar{\\alpha}_T = \\bar{\\beta}_T = 1$ . This implies that the two coefficients  $\\alpha_t$  and  $\\beta_t$  are not arbitrary transformations; rather, they should satisfy a specific sum constraint. Then, we redefine the conditional Markov diffusion process similar to the directional label forward distribution  $q$  without condition (detailed theoretical framework in Appendix C), assuming that when conditioned on features  $\\mathbf{x}$ , the prior distribution of  $\\hat{q}$  is the same as  $q$ :",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\hat {q} \\left(\\mathbf {y} _ {t} \\mid \\mathbf {y} _ {t - 1}, \\mathbf {y} _ {d}, \\mathbf {x}\\right) := q \\left(\\mathbf {y} _ {t} \\mid \\mathbf {y} _ {t - 1}, \\mathbf {y} _ {d}\\right) \\tag {8} \\\\ = \\mathcal {N} \\left(\\mathbf {y} _ {t}; \\mathbf {y} _ {t - 1} + \\alpha_ {t} \\mathbf {y} _ {d}, \\beta_ {t} ^ {2} \\mathbf {I}\\right), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\hat {q} \\left(\\mathbf {y} _ {1: T} \\mid \\mathbf {y} _ {0}, \\mathbf {y} _ {d}, \\mathbf {x}\\right) := \\prod_ {t = 1} ^ {T} \\hat {q} \\left(\\mathbf {y} _ {t} \\mid \\mathbf {y} _ {t - 1}, \\mathbf {y} _ {d}, \\mathbf {x}\\right) \\tag {9} \\\\ = \\mathcal {N} \\left(\\mathbf {y} _ {t}; \\mathbf {y} _ {0} + \\bar {\\alpha} _ {t} \\mathbf {y} _ {d}, \\bar {\\beta} _ {t} ^ {2} \\mathbf {I}\\right), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            539,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which means that the diffusion process of the labels is not influenced by any image features.",
+        "bbox": [
+            511,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In Appendix C, using Bayes' rule and Taylor expansion, we derive the conditional posterior distribution during the forward process:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {q} \\left(\\mathbf {y} _ {t - 1} \\mid \\mathbf {y} _ {t}, \\mathbf {y} _ {0}, \\mathbf {y} _ {d}, \\mathbf {x}\\right) = \\mathcal {N} \\left(\\mathbf {y} _ {t - 1}; \\hat {\\mu} _ {t}, \\hat {\\sigma} _ {t} \\mathbf {I}\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            544,
+            598,
+            903,
+            616
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{\\mu}_t = y_t - \\alpha_t y_d - \\frac{\\beta_t^2}{\\beta_t} \\epsilon + \\hat{\\sigma}_t \\nabla_{y_{t-1}} \\log \\hat{q}(\\mathbf{x} | \\mathbf{y}_{t-1}, \\mathbf{y}_d)$  and  $\\hat{\\sigma}_t = \\frac{\\beta_t^2 \\bar{\\beta}_{t-1}^2}{\\beta_t^2}$ . The last term in  $\\hat{\\mu}_t$  can be considered a deviation to the unconditional distribution mean, guided by the first derivative of  $\\hat{q}(\\mathbf{x} | \\mathbf{y}_{t-1}, \\mathbf{y}_d)$ , indicating that the decoding information from  $\\mathbf{y}_{t-1}$  to  $\\mathbf{x}$  should be introduced in training.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.3. Reverse and Training Process of DLD",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Reverse Process and Training. In the reverse (generation) process, as indicated by Eq. 6, we need to simultaneously predict  $\\mathbf{y}_d$  and  $\\epsilon$  to progressively recover  $\\mathbf{y}_T$  to  $\\mathbf{y}_0$ . Therefore, we can train two independent networks to estimate  $\\mathbf{y}_d^{\\theta_1}$  and  $\\epsilon_{\\theta_2}$ , respectively, to compute the reverse posterior distribution. Furthermore, we directly use feature information as input for two networks:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\theta} \\left(\\mathbf {y} _ {t - 1} \\mid \\mathbf {y} _ {t}, \\mathbf {x}\\right) := \\mathcal {N} \\left(\\mathbf {y} _ {t - 1}; \\mu_ {\\theta}, \\hat {\\sigma} _ {t} ^ {2} \\mathbf {I}\\right). \\tag {11}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
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+    {
+        "type": "page_number",
+        "text": "25741",
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+    {
+        "type": "image",
+        "img_path": "images/e97e2bb5b87d4508df05e432f7987aa9cc5744c0ac32100494bd5f996e06b6d5.jpg",
+        "image_caption": [
+            "Figure 2. Overview of the DLD framework. During Stage 1, the noisy dataset is quickly divided into three subsets. Then, we estimate  $\\mathbf{y}_0$  and  $\\mathbf{y}_n$  for each samples based on Eq. 14 and Eq. 15. In Stage 2, the label information and augmented features from Stage 1 are jointly used to train a directional diffusion model (blue bars represent random diffusion and gray bars represent directional diffusion)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Based on the analysis of the forward process, we adopt a straightforward approach which naturally integrates the decoding process into the diffusion model architecture by a fixed decoding layer  $L_{1}$  to map  $\\mathbf{y}$  into the feature space of  $\\mathbf{x}$ . Detailed information about the specific diffusion model network structure is shown in Appendix Figure C.1.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "By optimizing the VLB and reparameterization [21], we derive the following simplified loss function for training:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {d} = \\left\\| \\mathbf {y} _ {d} - \\mathbf {y} _ {d} ^ {\\theta_ {1}} \\left(\\mathbf {y} _ {t}, \\mathbf {y} _ {n}, \\mathbf {x}, t\\right) \\right\\| ^ {2}, \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\epsilon} = \\left\\| \\epsilon - \\epsilon_ {\\theta_ {2}} \\left(\\mathbf {y} _ {t}, \\mathbf {y} _ {n}, \\mathbf {x}, t\\right) \\right\\| ^ {2}, \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$ , and the training input  $\\mathbf{y}_t$  is synthesized using Eq. 7. Algorithm 1 describes the training procedure.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inference. Since the classification diffusion model is deterministic in inference and the dimensionality of the label vector is much lower than that of images, we mimic the inference process of DDIM [44] to generate labels in as few steps as possible without affecting the generated categories. We can gradually sample labels step-by-step following  $\\mathbf{y}_{t-1} = \\mathbf{y}_t - (\\bar{\\alpha}_t - \\bar{\\alpha}_{t-1})\\mathbf{y}_d^{\\theta_1} - (\\bar{\\beta}_t - \\bar{\\beta}_{t-1})\\epsilon_{\\theta_2}$ , where the transition from  $t-1$  to  $t$  is discrete rather than continuous in time. Appendix D provides a detailed explanation of the de-Markovization process, the accelerated sampling algorithm and the visual demonstration of the sampling process. In experiments, we use 5 steps for DLD's inference, which is on the same order of magnitude as the speed of traditional classification models.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Label Pre-correction Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Although diffusion models are powerful, under the guidance of incorrect  $\\mathbf{y}_0$  and  $\\mathbf{y}_n$ , they can easily fit the wrong conditional distributions. Therefore, we propose a one-step label pre-correction method that automatically provides accurate label information and feature conditions for the DLD model, requiring no additional parameter training, making it simple, straightforward, and efficient.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Label Pre-correction for  $\\mathbf{y}_0$ . Inspired by the concepts of multi-view[42, 53] and neighbor consistency regularization [22], our primary assumption is that the same sample should have similar neighborhood label distributions in different feature spaces. We define the original noisy dataset as  $\\mathcal{D} = \\{(x_i,\\tilde{y}_i)\\mid x_i\\in \\mathbb{R}^d,\\tilde{y}_i\\in \\mathbb{R}^m,i = 1,\\ldots ,n\\}$ . To obtain different feature spaces by a shared feature extractor  $f_{ext}$ , we first apply two different data augmentation methods and map them into  $\\mathbb{R}^w$  and  $\\mathbb{R}^s$ , with the augmented datasets respectively denoted as  $\\mathcal{D}^w$  and  $\\mathcal{D}^s$ . Then, we use Euclidean or Cosine similarity to obtain the nearest  $K$  neighborhood labels  $y_{k = 1}^{K}$  and feature space distances  $v_{k = 1}^{K}$  then we can get two weighted label distributions  $p_w$  and  $p_s$  by  $p(y_{i}) = \\left(\\sum_{k = 1}^{K}w_{k}\\cdot \\mathbf{1}(y_{k} = y_{i})\\right)\\cdot \\left(\\sum_{k = 1}^{K}w_{k}\\right)^{-1}$  where  $w_{k} = \\frac{1}{v_{k} + \\delta}$ , where  $\\delta$  is a small constant to prevent division by zero. Next, we calculate the divergence between the two distributions using the Kullback-Leibler divergence and a via Gaussian mixture model (GMM) [38] to re-partitioning three types of samples: Samples with high means are reassigned to the hard set  $\\mathcal{D}_H$ , which represents",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "25742",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "samples whose correctness is hard to determine and typically lie at the boundaries of classes. Samples with low means indicate that similar neighborhood distributions under both views. Using the principle of neighborhood consistency, we compare  $\\text{argmax}(p_{ws})$  with the original label  $\\tilde{y}$ , where  $p_{ws} = \\frac{p_w + p_s}{2}$ . If the class with the highest frequency in the average neighborhood distribution matches the original label, then the sample is assigned to the clean set  $\\mathcal{D}_C$ ; otherwise, it is assigned to the noisy set  $\\mathcal{D}_N$ .",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Based on the repartitioned sample subsets and the original noisy labels  $\\tilde{y}$ , we define a label pre-corrector, which functions similarly to a transition matrix. It can automatically perform label flipping or refinement:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP \\left(y _ {0} \\mid \\tilde {y}, x\\right) = \\left\\{ \\begin{array}{l l} \\tilde {y} & \\text {i f} x \\in \\mathcal {D} _ {C}, \\\\ \\operatorname {a r g m a x} \\left(p _ {w s}\\right) & \\text {i f} x \\in \\mathcal {D} _ {N}, \\\\ p _ {w s} & \\text {i f} x \\in \\mathcal {D} _ {H}. \\end{array} \\right. \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "According to Eq. 14, for samples with deterministic neighborhood label distributions, we use hard labels to minimize the interference of redundant information on  $y_0$ . For samples with more contentious neighborhood label distributions, we adopt a soft strategy for label refinement. Instead of point estimation, we estimate through a label vector, retaining most of the neighborhood information. This strategy enhances the accuracy of the  $y_0$  while preserving as much robust information as possible.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Estimate Noise distribution for  $\\mathbf{y}_n$ . Similar to obtaining  $\\mathbf{y}_0$ , we use the subset of divided samples to estimate the noise distribution of the samples. According to Eq. 15, when a sample is identified as clean, the directed diffusion term is used to gradually fade out  $\\mathbf{y}_0$  ( $\\mathbf{y}_d = -\\mathbf{y}_0$ ), allowing the model to learn to recover a label closer to the ground truth from an uninformed  $\\epsilon$ . When the sample contains noise, the endpoint of diffusion should include a clear representation of noise, enabling the model to strictly avoid recovering such noisy vector values during reverse generation. For uncertain samples, we simulate potential noise distributions by retaining the difference in label distributions between two views. The greater the difference in the distribution values for a particular class in the two views, the more likely the sample is incorrectly labeled as that class.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP \\left(y _ {n} \\mid \\tilde {y}, x\\right) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} x \\in \\mathcal {D} _ {C}, \\\\ \\tilde {y} & \\text {i f} x \\in \\mathcal {D} _ {N}, \\\\ \\frac {\\left| p _ {w} - p _ {s} \\right|}{\\sum \\left| p _ {w} - p _ {s} \\right|} & \\text {i f} x \\in \\mathcal {D} _ {H}. \\end{array} \\right. \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The complete training process is outlined in Algorithm 1, consisting of the following phases: Steps  $1 \\sim 3$  for sample re-partitioning, Steps  $4 \\sim 9$  for diffusion model training, with Step 6 dedicated to  $\\mathbf{y}_0$  pre-correction and  $\\mathbf{y}_n$  estimation. Notably, in Step 5, instead of sampling features from the original noisy set  $\\mathcal{D}$ , we use a mixture of sample features from  $\\mathcal{D}^w$  and  $\\mathcal{D}^s$  as the training input for the diffusion",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 DLD Training",
+        "text_level": 1,
+        "bbox": [
+            514,
+            90,
+            700,
+            106
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Input: Noisy training set  $\\mathcal{D} = \\{\\mathbf{X},\\tilde{\\mathbf{Y}}\\}$ , feature extractor  $f_{\\mathrm{ext}}$ , two network parameters  $\\theta_{1}$  and  $\\theta_{2}$",
+        "bbox": [
+            513,
+            109,
+            903,
+            140
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Output:  $\\theta_{1}$  and  $\\theta_{2}$",
+        "bbox": [
+            514,
+            141,
+            640,
+            155
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: Obtain two augmented features  $\\mathcal{D}^w$  and  $\\mathcal{D}^s$  using the feature extractor  $f_{\\mathrm{ext}}$ .",
+            "2: Calculate K-nearest label distributions  $p_w$  and  $p_s$ .",
+            "3: Re-partitioning samples into  $\\mathcal{D}_C, \\mathcal{D}_N$  and  $\\mathcal{D}_H$ .",
+            "4: while not converged do",
+            "5: Sample data  $(\\mathbf{x}_{ws},\\tilde{\\mathbf{y}})\\sim \\{\\mathcal{D}^w,\\mathcal{D}^s\\}$  ; time slice  $t\\sim$ $\\{1,\\dots ,T\\}$  ; and noise  $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$",
+            "6: Pre-estimate  $\\mathbf{y}_0$  and  $\\mathbf{y}_n$  based on Eq. 14 and Eq. 15, respectively.",
+            "7: Accumulate losses through Eq. 12 and Eq. 13.",
+            "8: Take gradient descent step on the losses to update network parameters.",
+            "9: end while"
+        ],
+        "bbox": [
+            521,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "model, where  $\\mathbf{x}_{ws} = (1 - \\gamma)\\mathbf{x}_w + \\gamma \\mathbf{x}_s$ , with  $\\gamma = \\frac{|\\mathcal{D}_H|}{|\\mathcal{D}|}$  representing the proportion of uncertain samples, which means that the more difficult the sample classification, the richer the feature conditions the model automatically introduces. This reflects an implicit regularization method that mitigates the issue of the diffusion model being overly confident when still learning incorrect information.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experimental Results and Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first evaluate the DLD's effectiveness on CIFAR datasets with varying levels of IDN in Section 5.1. Then, We conduct ablation studies in Section 5.2 to analyze the contributions of the pre-trained feature extractor, the label pre-correction technology, and other components. In Section 5.3, we compare the DLD to the SOTA methods across four real-world noisy datasets. Appendix E provides more details about our experiments.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Results on Simulated Noisy Datasets",
+        "text_level": 1,
+        "bbox": [
+            511,
+            652,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on the CIFAR-10 and CIFAR-100 datasets [27] with simulated IDN [6]. Details of the IDN generation algorithm and examples are provided in Appendix E.1. In our experiments, we generate noise levels of  $20\\%$ ,  $40\\%$ , and  $60\\%$ . To obtain the feature space for label pre-correction, we provide multiple configurations of feature extractors, including DLD+ResNet, DLD+SimCLR and DLD+ViT (see Appendix F.2 for detailed settings).",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As shown in Table 1, the DLD+ResNet configuration outperforms the baseline across most noise levels on CIFAR, especially in high-noise environments. We analyze that the main factor affecting its performance in low noise environment is the introduction of too much robust information, which leads to the interference of the model. When using the DLD+ViT configuration, its performance surpasses",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "25743",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/1bf87349bc6108a20b0cc43e23ffbb4c475582bd095e76175d2b195376dc57b4.jpg",
+        "table_caption": [
+            "Table 1. Classification accuracies (%) of CIFAR datasets under different levels of IDN."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">CIFAR-10</td><td colspan=\"3\">CIFAR-100</td></tr><tr><td>20%</td><td>40%</td><td>60%</td><td>20%</td><td>40%</td><td>60%</td></tr><tr><td>Co-teaching [17]</td><td>87.28±0.20</td><td>78.72±0.47</td><td>62.51±1.98</td><td>69.26±0.39</td><td>59.53±0.57</td><td>46.80±0.51</td></tr><tr><td>GCE [61]</td><td>86.44±0.23</td><td>76.71±0.39</td><td>60.76±3.08</td><td>68.24±0.27</td><td>55.76±1.18</td><td>46.75±2.46</td></tr><tr><td>DAC [45]</td><td>86.16±0.13</td><td>74.80±0.32</td><td>59.97±0.90</td><td>68.70±0.78</td><td>55.71±1.01</td><td>46.29±3.35</td></tr><tr><td>DMI [54]</td><td>86.57±0.16</td><td>77.81±0.85</td><td>69.94±1.31</td><td>68.71±1.21</td><td>57.99±0.92</td><td>50.96±2.08</td></tr><tr><td>SEAL [6]</td><td>87.79±0.09</td><td>82.98±0.05</td><td>70.07±1.54</td><td>70.61±0.19</td><td>61.18±0.35</td><td>51.86±1.32</td></tr><tr><td>NCR [22]</td><td>87.74±0.15</td><td>83.03±0.21</td><td>69.44±1.01</td><td>70.68±0.37</td><td>61.93±0.54</td><td>49.13±2.77</td></tr><tr><td>CC+DivideMix [62]</td><td>88.36±0.11</td><td>84.18±0.40</td><td>71.52±1.73</td><td>70.09±0.19</td><td>64.35±0.35</td><td>53.20±0.66</td></tr><tr><td>DISC [31]</td><td>90.68±0.10</td><td>85.61±0.32</td><td>73.59±1.13</td><td>71.49±0.13</td><td>64.46±0.29</td><td>53.62±0.51</td></tr><tr><td>LRA-diffusion+ResNet [4]</td><td>89.94±0.15</td><td>86.73±0.37</td><td>74.66±1.02</td><td>72.35±0.14</td><td>65.55±0.30</td><td>54.43±0.53</td></tr><tr><td>DLD+ResNet (Ours)</td><td>90.43±0.12</td><td>87.17±0.29</td><td>76.07±1.10</td><td>72.60±0.15</td><td>66.59±0.31</td><td>55.72±0.24</td></tr><tr><td>EPL+ViT [26]</td><td>95.95±0.17</td><td>93.01±0.33</td><td>76.16±1.18</td><td>72.24±0.12</td><td>67.20±0.20</td><td>55.59±0.13</td></tr><tr><td>LRA-diffusion+ViT [4]</td><td>96.65±0.18</td><td>93.68±0.34</td><td>78.12±1.17</td><td>73.59±0.13</td><td>67.67±0.21</td><td>57.21±0.12</td></tr><tr><td>DLD+ViT (Ours)</td><td>96.98±0.12</td><td>96.49±0.07</td><td>83.14±0.81</td><td>78.62±0.11</td><td>76.03±0.14</td><td>69.57±0.17</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "EPL+ViT and LRA-diffusion+ViT. This implies that DLD more effectively utilizes the provided prior knowledge without requiring additional training conditions. Across various datasets, DLD's superiority is more pronounced on CIFAR-100, indicating that the more complex IDN on CIFAR-100 severely impacts the performance of other methods, whereas our model maintains robust learning.",
+        "bbox": [
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+            368,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Additionally, we conducted experiments on the simulated CCN dataset. The results (see Appendix E.2) show that CCN is easier to handle than IDN, which aligns with our expectations. Compared to other methods, DLD still achieves the highest classification accuracy. Due to the lightweight architecture of the diffusion model and the single-step pre-correction process, DLD outperforms traditional LNL methods without incurring significant computational overhead. A detailed analysis of training time overhead and model parameters is provided in Appendix E.3.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
+            89,
+            636,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Power of label pre-correction. We validate the effectiveness of label pre-correction by freezing the diffusion model. As shown in Figure 3, our pre-correction method consistently outperforms in various noisy environments, while Figure 3b demonstrates that the LRA estimation method disrupts originally correct labels. Then, we unfroze the diffusion model to verify that DLD does not fully depend on the pre-correction method. Results show that DLD further enhances generalization performance based on pre-correction, indicating that the two methods complement each other effectively. Additionally, we design more comprehensive cross-ablation experiments, e.g., replacing the LRA technique in LRA-diffusion with the pre-correction module to demonstrate the necessity of directional diffusion. See Appendix F.1 for more details.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Contribution of different pre-trained features and other",
+        "bbox": [
+            89,
+            885,
+            482,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/d8aeea1dae7b845f36b039d219ba80f9232e176804ce280ca4353596adad6cbf.jpg",
+        "table_caption": [
+            "Table 2. Classification accuracies (%) on Animal-10N."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Accuracy</td></tr><tr><td>CE [35]</td><td>80.6</td></tr><tr><td>GCE [61]</td><td>81.5</td></tr><tr><td>NCT [8]</td><td>84.1</td></tr><tr><td>DISC [31]</td><td>87.3</td></tr><tr><td>SSR [14]</td><td>88.5</td></tr><tr><td>LRA-diffusion [4]</td><td>88.6</td></tr><tr><td>J-ViT [9]</td><td>89.0</td></tr><tr><td>DLD (Ours)</td><td>89.4</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "training components. We explore the impact of various feature extractors, including ResNet34 [20], SimCLR [7] and ViT-L/14 [40], and conduct ablation studies comparing our method with CARD and LRA-diffusion. Here, DISC [31] served as a baseline that does not require any pretrained models. Detailed results and analyses are provided in Appendix F.2. Our findings reveal that DLD outperforms other diffusion models when combined with different pretrained models, achieving optimal performance when integrated with ViT-L/14. This underscores ViT-L/14's effectiveness in enhancing label pre-correction and facilitating diffusion model learning. Furthermore, Appendix F.3 details additional ablation studies on various hyperparameter settings. We validate the optimal training strategy for the DLD method and recommend this combination.",
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+        "text": "5.3. Results on Real-world Noisy Datasets",
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+        "text": "We select four real-world noisy datasets for our experiments to demonstrate the superior performance of DLD: Animal10N [43], Clothing1M [52], WebVision [30], and ImageNet ILSVRC2012 [41]. Comprehensive descriptions of these datasets and detailed experimental setups can be",
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+        "image_caption": [
+            "(a) Experimental results on the CIFAR-10 dataset"
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+        "image_caption": [
+            "(b) Experimental results on the CIFAR-100 dataset",
+            "Figure 3. Comparison of different label correction strategies' accuracies, where Baseline represents the proportion of clean labels."
+        ],
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+        "table_caption": [
+            "Table 3. Classification accuracies (%) on Clothing1M."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Accuracy</td></tr><tr><td>Co-teaching [17]</td><td>69.21</td></tr><tr><td>DMI [54]</td><td>72.46</td></tr><tr><td>DivideMix [28]</td><td>74.76</td></tr><tr><td>CC [62]</td><td>75.40</td></tr><tr><td>DISC [31]</td><td>74.79</td></tr><tr><td>EPL [26]</td><td>75.21</td></tr><tr><td>LRA-diffusion [4]</td><td>74.46</td></tr><tr><td>SANM [46]</td><td>75.63</td></tr><tr><td>DLD (Ours)</td><td>75.69</td></tr></table>",
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+        "type": "table",
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+        "table_caption": [
+            "Table 4. Classification accuracies (%) on WebVision and ILSVRC2012 datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>WebVision</td><td>ILSVRC12</td></tr><tr><td>Co-teaching [17]</td><td>63.58</td><td>61.48</td></tr><tr><td>DivideMix [28]</td><td>77.32</td><td>75.20</td></tr><tr><td>ELR [33]</td><td>77.78</td><td>70.29</td></tr><tr><td>EPL [26]</td><td>78.77</td><td>76.51</td></tr><tr><td>C2D [63]</td><td>79.42</td><td>78.57</td></tr><tr><td>CC [62]</td><td>79.36</td><td>76.08</td></tr><tr><td>DISC [31]</td><td>80.28</td><td>77.44</td></tr><tr><td>LRA-diffusion [4]</td><td>84.16</td><td>82.56</td></tr><tr><td>DLD (Ours)</td><td>84.51</td><td>83.74</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "found in Appendix E.4 and Appendix E.5, respectively. As demonstrated in Table 2, Table 3, and Table 4, DLD outperforms all SOTA methods across these datasets. Note that DLD's relative classification performance improved by  $7.26\\%$  and  $0.44\\%$  over J-ViT [9] and EPL [26], respectively, both employing the ViT architecture. Compared to LRA-diffusion, which also employs ViT and label diffusion models, DLD achieves varying degrees of performance improvement, demonstrating a more effective and reason-",
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+    {
+        "type": "text",
+        "text": "able use of prior knowledge and diffusion models. Besides, while ViT-L/14 improved performance on Clothing1M, Appendix G shows that other extractors like CC can be even more effective, highlighting our method's versatility with different LNL methods. Besides, DLD's performance advantage partly stems from the pre-correction method. In future work, we aim to integrate discriminative and generative paradigms, using diffusion models to refine pre-correction, generate label information, and enhance representational power and multimodal generalization. Appendix H discusses additional limitations and future directions.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper proposes DLD, a diffusion model specifically designed to learn effectively from noisy labels for robust classification. Our main idea is to decouple the label diffusion process into two channels: directional diffusion and random diffusion. This approach explicitly introduces noisy label information into the diffusion model for the first time, enabling the model to interpretably mitigate the generation of incorrect labels, thereby enhancing its ability to generalize from noisy to clean data. By incorporating our low-cost label pre-correction method, DLD can automatically select label diffusion information for each sample in diverse noisy environments, without requiring additional adjustments or iterations. Additionally, our model synergizes with various pre-trained large-scale models, like ViT, leveraging their prior knowledge more effectively than other methods. Experiments on simulated and real-world noisy datasets show that DLD surpasses conventional LNL methods in both accuracy and efficiency. By framing LNL within a generative model, our method bridges LNL with other learning frameworks. We believe this work will reduce the workload for practitioners handling large-scale, low-quality labeled data, benefiting the development of the image recognition field.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work was supported in part by the National Natural Science Foundation of China under Grant U21A20513, Grant 62476157, Grant 62276161, Grant 62276157 and Grant 62406179, and in part by the Key Research and Development Program of Shanxi Province under Grant 202202020101003 and the Fundamental Research Program of Shanxi Province under Grant 202403021222026.",
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2025/Directional Label Diffusion Model for Learning from Noisy Labels/133ce87a-4a21-4fe5-b113-05841acf1ebd_origin.pdf

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2025/Directional Label Diffusion Model for Learning from Noisy Labels/full.md

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+# Directional Label Diffusion Model for Learning from Noisy Labels
+
+Senyu Hou $^{1}$ , Gaoxia Jiang $^{1}$ , Jia Zhang $^{1}$ , Shangrong Yang $^{1}$ , Husheng Guo $^{1}$ , Yaqing Guo $^{1}$ , Wenjian Wang $^{2*}$
+
+$^{1}$ School of Computer and Information Technology, Shanxi University, China  
+ $^{2}$ Key Laboratory of Computational Intelligence and Chinese Information Processing Ministry of Education, Shanxi University, China
+
+{202312407005, 202412407035}@email.sxu.edu.cn
+
+{jianggaoxia, sryang, guohusheng, yqguo, wjwang}@sxu.edu.cn
+
+# Abstract
+
+In image classification, the label quality of training data critically influences model generalization, especially for deep neural networks (DNNs). Traditionally, learning from noisy labels (LNL) can improve the generalization of DNNs through complex architectures or a series of robust techniques, but its performance improvement is limited by the discriminative paradigm. Unlike traditional ways, we resolve the LNL problems from the perspective of robust label generation, based on diffusion models within the generative paradigm. To expand the diffusion model into a robust classifier that explicitly accommodates more noise knowledge, we propose a Directional Label Diffusion (DLD) model. It disentangles the diffusion process into two paths, i.e., directional diffusion and random diffusion. Specifically, directional diffusion simulates the corruption of true labels into a directed noise distribution, prioritizing the removal of likely noise, whereas random diffusion introduces inherent randomness to support label recovery. This architecture enable DLD to gradually infer labels from an initial random state, interpretably diverging from the specified noise distribution. To adapt the model to diverse noisy environments, we design a low-cost label precorrection method that automatically supplies more accurate label information to the diffusion model, without requiring manual intervention or additional iterations. Our approach outperforms state-of-the-art methods on both simulated and real-world noisy datasets. Code is available at https://github.com/SenyuHou/DLD.
+
+# 1. Introduction
+
+Deep neural networks (DNNs) have achieved notable success across key areas of machine learning, driven by the growth of datasets and the increase in model parameters.
+
+These models are primarily trained using supervised learning, which relies heavily on large volumes of labeled data [5]. However, real-world data often suffer from low-quality labels due to subjective errors like indistinguishable samples or objective errors such as incorrect label recording, making noisy labels a widespread issue [13, 55]. Studies have shown that the generalization capability of deep neural networks is adversely affected when trained with noisy labels [1, 59]. Consequently, it is crucial to develop methods for learning from noisy labels (LNL) on large-scale but low-quality datasets.
+
+Due to the varied distribution of label noise, historical research has classified it into class-conditional noise (CCN) and instance-dependent noise (IDN) [57]. Recent studies indicate that label noise in real datasets predominantly aligns with the IDN assumption, wherein noise is unevenly distributed and more likely in samples with similar features [2, 6, 10–12, 51]. To tackle these complex noise patterns, mainstream LNL methods employ strategies combining filtering and training approaches. Some studies demonstrate a phenomenon known as the memorization effect [1, 3, 29, 56], i.e., DNNs first learn from simple data before fitting to noisy samples. Based on this observation, sample selection strategies utilize confidence levels or prediction loss during training intervals to identify noisy samples [17, 24, 28, 58]. However, this strategy is inherently risky, as the timing of noise memorization varies across datasets and noise distributions, complicating the selection criteria [6, 39]. Consequently, mainline LNL methods can often be integrated with training strategies to enhance model robustness, employing techniques like label filtering [17, 36, 50, 58], label correction [47, 60, 64], robust loss [16, 48, 61], and semi-supervised learning [28]. Among these techniques, semi-supervised learning, by combining multiple approaches [34, 37, 49], often outperforms other LNL methods but is still constrained by the discriminative framework. Although some researches attempt to combine
+
+variational autoencoders (VAE) [25] with DivideMix [28] to address label noise [15], most methods remain focused on discriminative models.
+
+In this paper, we shift away from the traditional LNL perspective, proposing robust classification models using label diffusion models that focus on the generative modeling and deeply explores the generative relationship between features and labels. Under this paradigm, labels are generated by gradually refining an initial random guess. The uncertainty modeling in diffusion models inherently meets some robustness requirements, as random label generation can offset some noise interference [4, 18]. However, this type of diffusion process lacks information about noisy labels. Intrinsic uncertainty alone is insufficient to handle complex noisy environments. Inspired by the residual diffusion denoising models (RDDM) [32], we explore a novel Directional Label Diffusion (DLD) model that incorporates noisy label information into the diffusion process. In DLD, we decouple the diffusion process into two channels: directional diffusion and random diffusion (see Figure 1). The directional diffusion guides the initial label towards a more probable noise direction (e.g., a green automobile may be misclassified as a frog or other classes, as indicated by the probability distribution in the third column in Figure 1), while random diffusion retains the original diffusion mechanism. This approach injects information about which categories should not be generated into the label generation paradigm, enhancing the interpretability of the diffusion model's robust inference. Unlike conventional label diffusion, our diffusion process concludes with an endpoint that includes the potential noise distribution of the sample (i.e.,  $\mathbf{y}_T = \mathbf{y}_n + \epsilon$ ) and employs two independent coefficient schedules to control the diffusion speed of both channels.
+
+One challenge is that only noisy labels are available in practice for training, so neither  $\mathbf{y}_0$  nor  $\mathbf{y}_n$  can be obtained directly. Few researchers employed neighborhood detection techniques like KNN to re-estimate  $\mathbf{y}_0$  [4]. However, under the IDN assumption, neighborhood labels of noisy samples often contain similar errors, making naive label estimation methods unreliable and potentially causing  $\mathbf{y}_0$  to deviate from the ground truth (see Figure 3). To address these issues, we further propose a straightforward and efficient label pre-correction method that automatically provides diverse label information for diffusion model training. This framework employs feature extractors to identify the neighborhood label distribution of samples. Note that these extractors are either trained with self-supervised methods [7, 19, 65], which require few additional training iterations, or use pre-trained models without further training, thus remaining unaffected by label noise. Additionally, this pre-correction strategy allows the seamless integration of pre-trained large-scale models such as Sim-CLR [7] and vision transformer (ViT) [40] into our framework to further
+
+boost the performance. The main contributions of this work are summarized as follows:
+
+- We propose a novel Directional Label Diffusion (DLD) model that explicitly introduces interpretable noise information through a dual diffusion architecture, enabling robust learning of label generation patterns from noisy data.  
+- We design a fast label pre-correction method that automatically provides more accurate label information for the diffusion process and richer feature conditions for the generation process. By leveraging the consistency principle, this method pre-estimates the label distribution in a single iteration without incurring additional costs.  
+- We refine the paradigm for introducing feature conditions with rigorous theoretical deduction and provide complementary training strategies to enhance robustness further.  
+- We experimentally show that our model surpasses the state-of-the-art (SOTA) methods on both simulated and real-world noisy datasets, e.g.,  $6\% \sim 21\%$  accuracy improvement on the CIFAR-100 dataset with IDN.
+
+# 2. Related Work
+
+# 2.1. Learning from Noisy Labels
+
+Screening and training strategies are central to LNL methods, aiming to distinguish noisy from clean samples and to optimize model learning under noisy conditions. Screening strategies, like Co-teaching [17], select low-loss samples as clean, while DivideMix [28] uses a Gaussian mixture model to automatically identify clean samples during training. Confidence-based methods like CC [62] and DISC [31] classify samples with unreliable predictions as noisy, whereas neighbor consistency regularization (NCR) [22] promotes learning from samples with high neighbor consistency. Our pre-correction method is based on similarity constraints across multi-view label distributions and leverages a feature extractor to provide high-quality information to the diffusion model without requiring additional iterative training. For training, models such as SEAL [6] iteratively correct noisy labels, but this often risks worsening outcomes [23]. Robust loss functions, like mean absolute error (MAE) [16] and generalized cross entropy (GCE) [61], enhance resilience to noisy labels, while DAC [45] and DMI [54] offer advanced mutual information-based losses. Approaches like DivideMix [28] treat LNL as semi-supervised learning, supported by methods like CC [62], C2D [63], and ELR [33] to refine the process. Without complex iterations or loss design, our method utilizes a lightweight diffusion network and a simple L2 loss to quickly learn the feature-label generation relationship.
+
+# 2.2. Label Denoising Diffusion Models
+
+Diffusion models were initially designed for image generation tasks and can be understood through the lenses of score matching and dynamics. Ho et al. [21] introduced a
+
+![](images/c07b814ed34be5d0f57d0b65e23ec6f71e12a29dad6bf275b3b5b1a6c5210b02.jpg)  
+Figure 1. The proposed Directional Label Diffusion (DLD) model includes diagrams illustrating both the forward and reverse processes. In the forward process, diffusion is decoupled into two channels: random diffusion and directional diffusion. Random diffusion represents the transformation of  $\mathbf{y}_0$  into random Gaussian noise  $\epsilon$ , while directional diffusion describes the transformation of  $\mathbf{y}_0$  into a specific sample noise label distribution  $\mathbf{y}_n$ . Ultimately,  $\mathbf{y}_0$  diffuses to the endpoint  $\mathbf{y}_T = \mathbf{y}_0 + \epsilon$ . Notably, the features of the samples serve as control conditions, guiding the generation of labels only during the reverse process.
+
+more classical interpretative framework known as denoising diffusion probabilistic models (DDPM), which have been widely applied across diverse domains. RDDM expands the denoising-based diffusion models, initially uninterpretable for image restoration, into a unified and interpretable model for both image generation and restoration by introducing residuals. Classification and regression diffusion models (CARD) [18] reconstruct the classification as a conditional generative task, generating labels from dimensionally reduced image features via a pre-trained encoder. Building on CARD, label-retrieval-augmented (LRA) diffusion model [4] re-estimates the generation targets through neighbor label retrieval, improving label accuracy. Our model disentangles the diffusion process into directional and random diffusion channels, enhancing diffusion quality through precorrection, which leads to train a more robust label diffusion model.
+
+# 3. Preliminary
+
+In this section, we primarily introduce the label denoising diffusion models (LDDM), which is constructed based on the theoretical framework of the DDPM [21]. We start by defining the data distribution  $\mathbf{y}_0\sim q(\mathbf{y}_0)$  and a Markovian forward (diffusion) process  $q$  , which progressively adds Gaussian noise  $\epsilon \sim \mathcal{N}(0,\mathbf{I})$  to the labels based on diffusion strength  $\beta_{t}$  , diffusing label  $\mathbf{y}_0$  to  $\mathbf{y}_T$  ..
+
+$$
+q \left(\mathbf {y} _ {t} \mid \mathbf {y} _ {t - 1}\right) = \mathcal {N} \left(\mathbf {y} _ {t}; \sqrt {1 - \beta_ {t}} \mathbf {y} _ {t - 1}, \beta_ {t} \mathbf {I}\right), \tag {1}
+$$
+
+Under Bayes' theorem, one finds that the posterior distribution of the forward process can be represented as a Gaussian distribution with mean  $\tilde{\mu}_t(\mathbf{y}_t,\mathbf{y}_0)$  and variance  $\tilde{\beta}_t$  :
+
+$$
+q \left(\mathbf {y} _ {t - 1} \mid \mathbf {y} _ {t}, \mathbf {y} _ {0}\right) = \mathcal {N} \left(\mathbf {y} _ {t - 1}; \tilde {\mu} _ {t} \left(\mathbf {y} _ {t}, \mathbf {y} _ {0}\right), \tilde {\beta} _ {t} \mathbf {I}\right), \tag {2}
+$$
+
+where  $\tilde{\mu}_t(\mathbf{y}_t,\mathbf{y}_0) = \frac{\sqrt{\bar{\alpha}_{t - 1}}\beta_t}{1 - \bar{\alpha}_t}\mathbf{y}_0 + \frac{\sqrt{\alpha_t(1 - \bar{\alpha}_{t - 1})}}{1 - \bar{\alpha}_t}\mathbf{y}_t$  and  $\tilde{\beta}_t = \frac{1 - \bar{\alpha}_{t - 1}}{1 - \bar{\alpha}_t}\beta_t$ , In the reverse process, we naturally employ a neural network to perform Markovian inference from  $q(\mathbf{y}_T)$ , fitting the posterior distribution  $q(\mathbf{y}_{t - 1}|\mathbf{y}_t)$  through to  $\mathbf{y}_0$ . Since the variance of the posterior Gaussian distribution depends only on the diffusion strength corresponding to time  $t$ , the neural network focuses primarily on predicting and learning the mean:
+
+$$
+p _ {\theta} \left(\mathbf {y} _ {t - 1} \mid \mathbf {y} _ {t}\right) := \mathcal {N} \left(\mathbf {y} _ {t - 1}; \mu_ {\theta} \left(\mathbf {y} _ {t}, t\right), \tilde {\beta} _ {t} \mathbf {I}\right). \tag {3}
+$$
+
+To train this model such that  $p_{\theta}(\mathbf{y}_0)$  closely approximates  $q(\mathbf{y}_0)$ , we can optimize the variational lower bound (VLB), however, research [7] found that directly predicting the mean was not effective, so they reparameterized the estimation target, constraining the neural network to estimate the actual noise of the diffusion process and simplified the loss function:
+
+$$
+L _ {\text {s i m p l e}} := E _ {t \sim [ 1, T ], \mathbf {y} _ {0} \sim q (\mathbf {y} _ {0}), \epsilon \sim \mathcal {N} (0, \mathbf {I})} \left[ \| \epsilon - \epsilon_ {\theta} (\mathbf {y} _ {t}, t) \| ^ {2} \right]. \tag {4}
+$$
+
+During inference, we utilize the label noise estimated by the model, restoring the mean of the label at time  $t - 1$  to retrieve its distribution form, and then gradually performing random sampling until generating the label  $\mathbf{y}_0$ :
+
+$$
+\mathbf {y} _ {t - 1} = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {y} _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} (\mathbf {y} _ {t}, t)\right) + \sqrt {\tilde {\beta} _ {t}} \mathbf {z}, \tag {5}
+$$
+
+where  $\mathbf{z} \sim \mathcal{N}(0, \mathbf{I})$ . Unfortunately, this label generation process lacks any conditional information, resulting in random label generation for images with identical features, which fails to achieve classification. To address this, we
+
+analyze the foundational paradigm of conditional label diffusion models in Appendix A and simplify the method of feature conditioning.
+
+# 4. Directional Label Diffusion Model
+
+Based on LDDM, our goal is to develop a directional diffusion process on labels to introduce more knowledge about noise. We modify the representation of  $\mathbf{y}_T = \epsilon$  in LDDM to  $\mathbf{y}_T = \mathbf{y}_n + \epsilon$  in our DLD, where  $\mathbf{y}_n$  is an estimation of noisy label distribution. The improved forward process is no longer a simple random noise diffusion but is disentangled into two paths of directional diffusion and random diffusion, as shown in Figure 1.
+
+In the following subsections, we first outline the overall framework of our model in Section 4.1. Next, in Section 4.2, we present the foundational theory of the DLD diffusion process and analyze the method of conditional control. In Section 4.3, we describe the reverse process and training method, including optimizations for introducing feature conditions and an adapted accelerated inference method. Finally, in Section 4.4, we describe the rapid label pre-correction method within the DLD framework.
+
+# 4.1. Model Overview
+
+We propose the Directional Label Diffusion (DLD) framework, with the overall process illustrated in Figure 2. The framework contains two main stages: label pre-correction (Stage 1) and the directional label diffusion model (Stage 2). In stage 1, we first use two different data augmentation methods to provide two views for each sample, then use a pre-trained feature extractor  $f_{ext}$  to observe the neighborhood label distribution  $p_w$  and  $p_s$  of the same sample in two feature spaces. Based on similarity constraints and the principle of neighborhood consistency, we divide the dataset into clean, noisy, and hard sets. Then, the label precorrector and noise distribution estimator prepare  $\mathbf{y}_0$  and  $\mathbf{y}_n$  based on the sample partitioning results, using  $\mathbf{y}_0$  as the initial diffusion label and  $\mathbf{y}_n$  as part of the diffusion endpoint for the next stage of model training. Otherwise, we introduce both augmented image features and high-quality features extracted by  $f_{ext}$  into the training process to jointly guide the learning of the robust diffusion model.
+
+# 4.2. Forward Process of DLD
+
+To model the random diffusion of labels and the addition of directional noise information, we define the single forward (diffusion) process step in our DLD as follows:
+
+$$
+\mathbf {y} _ {t} = \mathbf {y} _ {t - 1} + \alpha_ {t} \mathbf {y} _ {d} + \beta_ {t} \epsilon , \tag {6}
+$$
+
+where  $\mathbf{y}_d$  is the deviation between  $\mathbf{y}_n$  and  $y_0$  (i.e.,  $\mathbf{y}_d = \mathbf{y}_n - \mathbf{y}_0$ ), representing the directional shift contained in the diffusion from  $\mathbf{y}_{t-1}$  to  $\mathbf{y}_t$ . Two independent coefficients,  $\alpha_t$
+
+and  $\beta_{t}$  control the degrees of directional and random diffusion, respectively. Based on the additivity of Gaussian noise, we derive the jump diffusion formula from  $\mathbf{y}_0$  to  $\mathbf{y}_t$  without requiring single-step continuous diffusion (see Appendix B for the proof):
+
+$$
+\mathbf {y} _ {t} = \mathbf {y} _ {0} + \bar {\alpha} _ {t} \mathbf {y} _ {d} + \bar {\beta} _ {t} \epsilon , \tag {7}
+$$
+
+where  $\bar{\alpha}_t = \sum_{i=1}^t \alpha_i$  and  $\bar{\beta}_t = \sqrt{\sum_{i=1}^t \beta_i^2}$ . When  $t = T$ , we hope  $\mathbf{y}_T = \mathbf{y}_n + \epsilon = \mathbf{y}_0 + \mathbf{y}_d + \epsilon$ , so we usually set  $\bar{\alpha}_T = \bar{\beta}_T = 1$ . This implies that the two coefficients  $\alpha_t$  and  $\beta_t$  are not arbitrary transformations; rather, they should satisfy a specific sum constraint. Then, we redefine the conditional Markov diffusion process similar to the directional label forward distribution  $q$  without condition (detailed theoretical framework in Appendix C), assuming that when conditioned on features  $\mathbf{x}$ , the prior distribution of  $\hat{q}$  is the same as  $q$ :
+
+$$
+\begin{array}{l} \hat {q} \left(\mathbf {y} _ {t} \mid \mathbf {y} _ {t - 1}, \mathbf {y} _ {d}, \mathbf {x}\right) := q \left(\mathbf {y} _ {t} \mid \mathbf {y} _ {t - 1}, \mathbf {y} _ {d}\right) \tag {8} \\ = \mathcal {N} \left(\mathbf {y} _ {t}; \mathbf {y} _ {t - 1} + \alpha_ {t} \mathbf {y} _ {d}, \beta_ {t} ^ {2} \mathbf {I}\right), \\ \end{array}
+$$
+
+$$
+\begin{array}{l} \hat {q} \left(\mathbf {y} _ {1: T} \mid \mathbf {y} _ {0}, \mathbf {y} _ {d}, \mathbf {x}\right) := \prod_ {t = 1} ^ {T} \hat {q} \left(\mathbf {y} _ {t} \mid \mathbf {y} _ {t - 1}, \mathbf {y} _ {d}, \mathbf {x}\right) \tag {9} \\ = \mathcal {N} \left(\mathbf {y} _ {t}; \mathbf {y} _ {0} + \bar {\alpha} _ {t} \mathbf {y} _ {d}, \bar {\beta} _ {t} ^ {2} \mathbf {I}\right), \\ \end{array}
+$$
+
+which means that the diffusion process of the labels is not influenced by any image features.
+
+In Appendix C, using Bayes' rule and Taylor expansion, we derive the conditional posterior distribution during the forward process:
+
+$$
+\hat {q} \left(\mathbf {y} _ {t - 1} \mid \mathbf {y} _ {t}, \mathbf {y} _ {0}, \mathbf {y} _ {d}, \mathbf {x}\right) = \mathcal {N} \left(\mathbf {y} _ {t - 1}; \hat {\mu} _ {t}, \hat {\sigma} _ {t} \mathbf {I}\right), \tag {10}
+$$
+
+where  $\hat{\mu}_t = y_t - \alpha_t y_d - \frac{\beta_t^2}{\beta_t} \epsilon + \hat{\sigma}_t \nabla_{y_{t-1}} \log \hat{q}(\mathbf{x} | \mathbf{y}_{t-1}, \mathbf{y}_d)$  and  $\hat{\sigma}_t = \frac{\beta_t^2 \bar{\beta}_{t-1}^2}{\beta_t^2}$ . The last term in  $\hat{\mu}_t$  can be considered a deviation to the unconditional distribution mean, guided by the first derivative of  $\hat{q}(\mathbf{x} | \mathbf{y}_{t-1}, \mathbf{y}_d)$ , indicating that the decoding information from  $\mathbf{y}_{t-1}$  to  $\mathbf{x}$  should be introduced in training.
+
+# 4.3. Reverse and Training Process of DLD
+
+Reverse Process and Training. In the reverse (generation) process, as indicated by Eq. 6, we need to simultaneously predict  $\mathbf{y}_d$  and  $\epsilon$  to progressively recover  $\mathbf{y}_T$  to  $\mathbf{y}_0$ . Therefore, we can train two independent networks to estimate  $\mathbf{y}_d^{\theta_1}$  and  $\epsilon_{\theta_2}$ , respectively, to compute the reverse posterior distribution. Furthermore, we directly use feature information as input for two networks:
+
+$$
+p _ {\theta} \left(\mathbf {y} _ {t - 1} \mid \mathbf {y} _ {t}, \mathbf {x}\right) := \mathcal {N} \left(\mathbf {y} _ {t - 1}; \mu_ {\theta}, \hat {\sigma} _ {t} ^ {2} \mathbf {I}\right). \tag {11}
+$$
+
+![](images/e97e2bb5b87d4508df05e432f7987aa9cc5744c0ac32100494bd5f996e06b6d5.jpg)  
+Figure 2. Overview of the DLD framework. During Stage 1, the noisy dataset is quickly divided into three subsets. Then, we estimate  $\mathbf{y}_0$  and  $\mathbf{y}_n$  for each samples based on Eq. 14 and Eq. 15. In Stage 2, the label information and augmented features from Stage 1 are jointly used to train a directional diffusion model (blue bars represent random diffusion and gray bars represent directional diffusion).
+
+Based on the analysis of the forward process, we adopt a straightforward approach which naturally integrates the decoding process into the diffusion model architecture by a fixed decoding layer  $L_{1}$  to map  $\mathbf{y}$  into the feature space of  $\mathbf{x}$ . Detailed information about the specific diffusion model network structure is shown in Appendix Figure C.1.
+
+By optimizing the VLB and reparameterization [21], we derive the following simplified loss function for training:
+
+$$
+\mathcal {L} _ {d} = \left\| \mathbf {y} _ {d} - \mathbf {y} _ {d} ^ {\theta_ {1}} \left(\mathbf {y} _ {t}, \mathbf {y} _ {n}, \mathbf {x}, t\right) \right\| ^ {2}, \tag {12}
+$$
+
+$$
+\mathcal {L} _ {\epsilon} = \left\| \epsilon - \epsilon_ {\theta_ {2}} \left(\mathbf {y} _ {t}, \mathbf {y} _ {n}, \mathbf {x}, t\right) \right\| ^ {2}, \tag {13}
+$$
+
+where  $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ , and the training input  $\mathbf{y}_t$  is synthesized using Eq. 7. Algorithm 1 describes the training procedure.
+
+Inference. Since the classification diffusion model is deterministic in inference and the dimensionality of the label vector is much lower than that of images, we mimic the inference process of DDIM [44] to generate labels in as few steps as possible without affecting the generated categories. We can gradually sample labels step-by-step following  $\mathbf{y}_{t-1} = \mathbf{y}_t - (\bar{\alpha}_t - \bar{\alpha}_{t-1})\mathbf{y}_d^{\theta_1} - (\bar{\beta}_t - \bar{\beta}_{t-1})\epsilon_{\theta_2}$ , where the transition from  $t-1$  to  $t$  is discrete rather than continuous in time. Appendix D provides a detailed explanation of the de-Markovization process, the accelerated sampling algorithm and the visual demonstration of the sampling process. In experiments, we use 5 steps for DLD's inference, which is on the same order of magnitude as the speed of traditional classification models.
+
+# 4.4. Label Pre-correction Method
+
+Although diffusion models are powerful, under the guidance of incorrect  $\mathbf{y}_0$  and  $\mathbf{y}_n$ , they can easily fit the wrong conditional distributions. Therefore, we propose a one-step label pre-correction method that automatically provides accurate label information and feature conditions for the DLD model, requiring no additional parameter training, making it simple, straightforward, and efficient.
+
+Label Pre-correction for  $\mathbf{y}_0$ . Inspired by the concepts of multi-view[42, 53] and neighbor consistency regularization [22], our primary assumption is that the same sample should have similar neighborhood label distributions in different feature spaces. We define the original noisy dataset as  $\mathcal{D} = \{(x_i,\tilde{y}_i)\mid x_i\in \mathbb{R}^d,\tilde{y}_i\in \mathbb{R}^m,i = 1,\ldots ,n\}$ . To obtain different feature spaces by a shared feature extractor  $f_{ext}$ , we first apply two different data augmentation methods and map them into  $\mathbb{R}^w$  and  $\mathbb{R}^s$ , with the augmented datasets respectively denoted as  $\mathcal{D}^w$  and  $\mathcal{D}^s$ . Then, we use Euclidean or Cosine similarity to obtain the nearest  $K$  neighborhood labels  $y_{k = 1}^{K}$  and feature space distances  $v_{k = 1}^{K}$  then we can get two weighted label distributions  $p_w$  and  $p_s$  by  $p(y_{i}) = \left(\sum_{k = 1}^{K}w_{k}\cdot \mathbf{1}(y_{k} = y_{i})\right)\cdot \left(\sum_{k = 1}^{K}w_{k}\right)^{-1}$  where  $w_{k} = \frac{1}{v_{k} + \delta}$ , where  $\delta$  is a small constant to prevent division by zero. Next, we calculate the divergence between the two distributions using the Kullback-Leibler divergence and a via Gaussian mixture model (GMM) [38] to re-partitioning three types of samples: Samples with high means are reassigned to the hard set  $\mathcal{D}_H$ , which represents
+
+samples whose correctness is hard to determine and typically lie at the boundaries of classes. Samples with low means indicate that similar neighborhood distributions under both views. Using the principle of neighborhood consistency, we compare  $\text{argmax}(p_{ws})$  with the original label  $\tilde{y}$ , where  $p_{ws} = \frac{p_w + p_s}{2}$ . If the class with the highest frequency in the average neighborhood distribution matches the original label, then the sample is assigned to the clean set  $\mathcal{D}_C$ ; otherwise, it is assigned to the noisy set  $\mathcal{D}_N$ .
+
+Based on the repartitioned sample subsets and the original noisy labels  $\tilde{y}$ , we define a label pre-corrector, which functions similarly to a transition matrix. It can automatically perform label flipping or refinement:
+
+$$
+P \left(y _ {0} \mid \tilde {y}, x\right) = \left\{ \begin{array}{l l} \tilde {y} & \text {i f} x \in \mathcal {D} _ {C}, \\ \operatorname {a r g m a x} \left(p _ {w s}\right) & \text {i f} x \in \mathcal {D} _ {N}, \\ p _ {w s} & \text {i f} x \in \mathcal {D} _ {H}. \end{array} \right. \tag {14}
+$$
+
+According to Eq. 14, for samples with deterministic neighborhood label distributions, we use hard labels to minimize the interference of redundant information on  $y_0$ . For samples with more contentious neighborhood label distributions, we adopt a soft strategy for label refinement. Instead of point estimation, we estimate through a label vector, retaining most of the neighborhood information. This strategy enhances the accuracy of the  $y_0$  while preserving as much robust information as possible.
+
+Estimate Noise distribution for  $\mathbf{y}_n$ . Similar to obtaining  $\mathbf{y}_0$ , we use the subset of divided samples to estimate the noise distribution of the samples. According to Eq. 15, when a sample is identified as clean, the directed diffusion term is used to gradually fade out  $\mathbf{y}_0$  ( $\mathbf{y}_d = -\mathbf{y}_0$ ), allowing the model to learn to recover a label closer to the ground truth from an uninformed  $\epsilon$ . When the sample contains noise, the endpoint of diffusion should include a clear representation of noise, enabling the model to strictly avoid recovering such noisy vector values during reverse generation. For uncertain samples, we simulate potential noise distributions by retaining the difference in label distributions between two views. The greater the difference in the distribution values for a particular class in the two views, the more likely the sample is incorrectly labeled as that class.
+
+$$
+P \left(y _ {n} \mid \tilde {y}, x\right) = \left\{ \begin{array}{l l} 0 & \text {i f} x \in \mathcal {D} _ {C}, \\ \tilde {y} & \text {i f} x \in \mathcal {D} _ {N}, \\ \frac {\left| p _ {w} - p _ {s} \right|}{\sum \left| p _ {w} - p _ {s} \right|} & \text {i f} x \in \mathcal {D} _ {H}. \end{array} \right. \tag {15}
+$$
+
+The complete training process is outlined in Algorithm 1, consisting of the following phases: Steps  $1 \sim 3$  for sample re-partitioning, Steps  $4 \sim 9$  for diffusion model training, with Step 6 dedicated to  $\mathbf{y}_0$  pre-correction and  $\mathbf{y}_n$  estimation. Notably, in Step 5, instead of sampling features from the original noisy set  $\mathcal{D}$ , we use a mixture of sample features from  $\mathcal{D}^w$  and  $\mathcal{D}^s$  as the training input for the diffusion
+
+# Algorithm 1 DLD Training
+
+Input: Noisy training set  $\mathcal{D} = \{\mathbf{X},\tilde{\mathbf{Y}}\}$ , feature extractor  $f_{\mathrm{ext}}$ , two network parameters  $\theta_{1}$  and  $\theta_{2}$
+
+Output:  $\theta_{1}$  and  $\theta_{2}$
+
+1: Obtain two augmented features  $\mathcal{D}^w$  and  $\mathcal{D}^s$  using the feature extractor  $f_{\mathrm{ext}}$ .  
+2: Calculate K-nearest label distributions  $p_w$  and  $p_s$ .  
+3: Re-partitioning samples into  $\mathcal{D}_C, \mathcal{D}_N$  and  $\mathcal{D}_H$ .  
+4: while not converged do  
+5: Sample data  $(\mathbf{x}_{ws},\tilde{\mathbf{y}})\sim \{\mathcal{D}^w,\mathcal{D}^s\}$  ; time slice  $t\sim$ $\{1,\dots ,T\}$  ; and noise  $\epsilon \sim \mathcal{N}(0,\mathbf{I})$  
+6: Pre-estimate  $\mathbf{y}_0$  and  $\mathbf{y}_n$  based on Eq. 14 and Eq. 15, respectively.  
+7: Accumulate losses through Eq. 12 and Eq. 13.  
+8: Take gradient descent step on the losses to update network parameters.  
+9: end while
+
+model, where  $\mathbf{x}_{ws} = (1 - \gamma)\mathbf{x}_w + \gamma \mathbf{x}_s$ , with  $\gamma = \frac{|\mathcal{D}_H|}{|\mathcal{D}|}$  representing the proportion of uncertain samples, which means that the more difficult the sample classification, the richer the feature conditions the model automatically introduces. This reflects an implicit regularization method that mitigates the issue of the diffusion model being overly confident when still learning incorrect information.
+
+# 5. Experimental Results and Analysis
+
+In this section, we first evaluate the DLD's effectiveness on CIFAR datasets with varying levels of IDN in Section 5.1. Then, We conduct ablation studies in Section 5.2 to analyze the contributions of the pre-trained feature extractor, the label pre-correction technology, and other components. In Section 5.3, we compare the DLD to the SOTA methods across four real-world noisy datasets. Appendix E provides more details about our experiments.
+
+# 5.1. Results on Simulated Noisy Datasets
+
+We conduct experiments on the CIFAR-10 and CIFAR-100 datasets [27] with simulated IDN [6]. Details of the IDN generation algorithm and examples are provided in Appendix E.1. In our experiments, we generate noise levels of  $20\%$ ,  $40\%$ , and  $60\%$ . To obtain the feature space for label pre-correction, we provide multiple configurations of feature extractors, including DLD+ResNet, DLD+SimCLR and DLD+ViT (see Appendix F.2 for detailed settings).
+
+As shown in Table 1, the DLD+ResNet configuration outperforms the baseline across most noise levels on CIFAR, especially in high-noise environments. We analyze that the main factor affecting its performance in low noise environment is the introduction of too much robust information, which leads to the interference of the model. When using the DLD+ViT configuration, its performance surpasses
+
+Table 1. Classification accuracies (%) of CIFAR datasets under different levels of IDN.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">CIFAR-10</td><td colspan="3">CIFAR-100</td></tr><tr><td>20%</td><td>40%</td><td>60%</td><td>20%</td><td>40%</td><td>60%</td></tr><tr><td>Co-teaching [17]</td><td>87.28±0.20</td><td>78.72±0.47</td><td>62.51±1.98</td><td>69.26±0.39</td><td>59.53±0.57</td><td>46.80±0.51</td></tr><tr><td>GCE [61]</td><td>86.44±0.23</td><td>76.71±0.39</td><td>60.76±3.08</td><td>68.24±0.27</td><td>55.76±1.18</td><td>46.75±2.46</td></tr><tr><td>DAC [45]</td><td>86.16±0.13</td><td>74.80±0.32</td><td>59.97±0.90</td><td>68.70±0.78</td><td>55.71±1.01</td><td>46.29±3.35</td></tr><tr><td>DMI [54]</td><td>86.57±0.16</td><td>77.81±0.85</td><td>69.94±1.31</td><td>68.71±1.21</td><td>57.99±0.92</td><td>50.96±2.08</td></tr><tr><td>SEAL [6]</td><td>87.79±0.09</td><td>82.98±0.05</td><td>70.07±1.54</td><td>70.61±0.19</td><td>61.18±0.35</td><td>51.86±1.32</td></tr><tr><td>NCR [22]</td><td>87.74±0.15</td><td>83.03±0.21</td><td>69.44±1.01</td><td>70.68±0.37</td><td>61.93±0.54</td><td>49.13±2.77</td></tr><tr><td>CC+DivideMix [62]</td><td>88.36±0.11</td><td>84.18±0.40</td><td>71.52±1.73</td><td>70.09±0.19</td><td>64.35±0.35</td><td>53.20±0.66</td></tr><tr><td>DISC [31]</td><td>90.68±0.10</td><td>85.61±0.32</td><td>73.59±1.13</td><td>71.49±0.13</td><td>64.46±0.29</td><td>53.62±0.51</td></tr><tr><td>LRA-diffusion+ResNet [4]</td><td>89.94±0.15</td><td>86.73±0.37</td><td>74.66±1.02</td><td>72.35±0.14</td><td>65.55±0.30</td><td>54.43±0.53</td></tr><tr><td>DLD+ResNet (Ours)</td><td>90.43±0.12</td><td>87.17±0.29</td><td>76.07±1.10</td><td>72.60±0.15</td><td>66.59±0.31</td><td>55.72±0.24</td></tr><tr><td>EPL+ViT [26]</td><td>95.95±0.17</td><td>93.01±0.33</td><td>76.16±1.18</td><td>72.24±0.12</td><td>67.20±0.20</td><td>55.59±0.13</td></tr><tr><td>LRA-diffusion+ViT [4]</td><td>96.65±0.18</td><td>93.68±0.34</td><td>78.12±1.17</td><td>73.59±0.13</td><td>67.67±0.21</td><td>57.21±0.12</td></tr><tr><td>DLD+ViT (Ours)</td><td>96.98±0.12</td><td>96.49±0.07</td><td>83.14±0.81</td><td>78.62±0.11</td><td>76.03±0.14</td><td>69.57±0.17</td></tr></table>
+
+EPL+ViT and LRA-diffusion+ViT. This implies that DLD more effectively utilizes the provided prior knowledge without requiring additional training conditions. Across various datasets, DLD's superiority is more pronounced on CIFAR-100, indicating that the more complex IDN on CIFAR-100 severely impacts the performance of other methods, whereas our model maintains robust learning.
+
+Additionally, we conducted experiments on the simulated CCN dataset. The results (see Appendix E.2) show that CCN is easier to handle than IDN, which aligns with our expectations. Compared to other methods, DLD still achieves the highest classification accuracy. Due to the lightweight architecture of the diffusion model and the single-step pre-correction process, DLD outperforms traditional LNL methods without incurring significant computational overhead. A detailed analysis of training time overhead and model parameters is provided in Appendix E.3.
+
+# 5.2. Ablation Studies
+
+Power of label pre-correction. We validate the effectiveness of label pre-correction by freezing the diffusion model. As shown in Figure 3, our pre-correction method consistently outperforms in various noisy environments, while Figure 3b demonstrates that the LRA estimation method disrupts originally correct labels. Then, we unfroze the diffusion model to verify that DLD does not fully depend on the pre-correction method. Results show that DLD further enhances generalization performance based on pre-correction, indicating that the two methods complement each other effectively. Additionally, we design more comprehensive cross-ablation experiments, e.g., replacing the LRA technique in LRA-diffusion with the pre-correction module to demonstrate the necessity of directional diffusion. See Appendix F.1 for more details.
+
+Contribution of different pre-trained features and other
+
+Table 2. Classification accuracies (%) on Animal-10N.  
+
+<table><tr><td>Method</td><td>Accuracy</td></tr><tr><td>CE [35]</td><td>80.6</td></tr><tr><td>GCE [61]</td><td>81.5</td></tr><tr><td>NCT [8]</td><td>84.1</td></tr><tr><td>DISC [31]</td><td>87.3</td></tr><tr><td>SSR [14]</td><td>88.5</td></tr><tr><td>LRA-diffusion [4]</td><td>88.6</td></tr><tr><td>J-ViT [9]</td><td>89.0</td></tr><tr><td>DLD (Ours)</td><td>89.4</td></tr></table>
+
+training components. We explore the impact of various feature extractors, including ResNet34 [20], SimCLR [7] and ViT-L/14 [40], and conduct ablation studies comparing our method with CARD and LRA-diffusion. Here, DISC [31] served as a baseline that does not require any pretrained models. Detailed results and analyses are provided in Appendix F.2. Our findings reveal that DLD outperforms other diffusion models when combined with different pretrained models, achieving optimal performance when integrated with ViT-L/14. This underscores ViT-L/14's effectiveness in enhancing label pre-correction and facilitating diffusion model learning. Furthermore, Appendix F.3 details additional ablation studies on various hyperparameter settings. We validate the optimal training strategy for the DLD method and recommend this combination.
+
+# 5.3. Results on Real-world Noisy Datasets
+
+We select four real-world noisy datasets for our experiments to demonstrate the superior performance of DLD: Animal10N [43], Clothing1M [52], WebVision [30], and ImageNet ILSVRC2012 [41]. Comprehensive descriptions of these datasets and detailed experimental setups can be
+
+![](images/583fbcb0c2d28e4097d41b09173dd3eece8bb464b0de20c1edf1f9cfafa91618.jpg)  
+(a) Experimental results on the CIFAR-10 dataset
+
+![](images/7e01a5932844ab8d099133ec3ebdb8ff0faa62526609a98a5f2823c22774ac80.jpg)  
+(b) Experimental results on the CIFAR-100 dataset  
+Figure 3. Comparison of different label correction strategies' accuracies, where Baseline represents the proportion of clean labels.
+
+Table 3. Classification accuracies (%) on Clothing1M.  
+
+<table><tr><td>Method</td><td>Accuracy</td></tr><tr><td>Co-teaching [17]</td><td>69.21</td></tr><tr><td>DMI [54]</td><td>72.46</td></tr><tr><td>DivideMix [28]</td><td>74.76</td></tr><tr><td>CC [62]</td><td>75.40</td></tr><tr><td>DISC [31]</td><td>74.79</td></tr><tr><td>EPL [26]</td><td>75.21</td></tr><tr><td>LRA-diffusion [4]</td><td>74.46</td></tr><tr><td>SANM [46]</td><td>75.63</td></tr><tr><td>DLD (Ours)</td><td>75.69</td></tr></table>
+
+Table 4. Classification accuracies (%) on WebVision and ILSVRC2012 datasets.  
+
+<table><tr><td>Method</td><td>WebVision</td><td>ILSVRC12</td></tr><tr><td>Co-teaching [17]</td><td>63.58</td><td>61.48</td></tr><tr><td>DivideMix [28]</td><td>77.32</td><td>75.20</td></tr><tr><td>ELR [33]</td><td>77.78</td><td>70.29</td></tr><tr><td>EPL [26]</td><td>78.77</td><td>76.51</td></tr><tr><td>C2D [63]</td><td>79.42</td><td>78.57</td></tr><tr><td>CC [62]</td><td>79.36</td><td>76.08</td></tr><tr><td>DISC [31]</td><td>80.28</td><td>77.44</td></tr><tr><td>LRA-diffusion [4]</td><td>84.16</td><td>82.56</td></tr><tr><td>DLD (Ours)</td><td>84.51</td><td>83.74</td></tr></table>
+
+found in Appendix E.4 and Appendix E.5, respectively. As demonstrated in Table 2, Table 3, and Table 4, DLD outperforms all SOTA methods across these datasets. Note that DLD's relative classification performance improved by  $7.26\%$  and  $0.44\%$  over J-ViT [9] and EPL [26], respectively, both employing the ViT architecture. Compared to LRA-diffusion, which also employs ViT and label diffusion models, DLD achieves varying degrees of performance improvement, demonstrating a more effective and reason-
+
+able use of prior knowledge and diffusion models. Besides, while ViT-L/14 improved performance on Clothing1M, Appendix G shows that other extractors like CC can be even more effective, highlighting our method's versatility with different LNL methods. Besides, DLD's performance advantage partly stems from the pre-correction method. In future work, we aim to integrate discriminative and generative paradigms, using diffusion models to refine pre-correction, generate label information, and enhance representational power and multimodal generalization. Appendix H discusses additional limitations and future directions.
+
+# 6. Conclusion
+
+This paper proposes DLD, a diffusion model specifically designed to learn effectively from noisy labels for robust classification. Our main idea is to decouple the label diffusion process into two channels: directional diffusion and random diffusion. This approach explicitly introduces noisy label information into the diffusion model for the first time, enabling the model to interpretably mitigate the generation of incorrect labels, thereby enhancing its ability to generalize from noisy to clean data. By incorporating our low-cost label pre-correction method, DLD can automatically select label diffusion information for each sample in diverse noisy environments, without requiring additional adjustments or iterations. Additionally, our model synergizes with various pre-trained large-scale models, like ViT, leveraging their prior knowledge more effectively than other methods. Experiments on simulated and real-world noisy datasets show that DLD surpasses conventional LNL methods in both accuracy and efficiency. By framing LNL within a generative model, our method bridges LNL with other learning frameworks. We believe this work will reduce the workload for practitioners handling large-scale, low-quality labeled data, benefiting the development of the image recognition field.
+
+# Acknowledgements
+
+This work was supported in part by the National Natural Science Foundation of China under Grant U21A20513, Grant 62476157, Grant 62276161, Grant 62276157 and Grant 62406179, and in part by the Key Research and Development Program of Shanxi Province under Grant 202202020101003 and the Fundamental Research Program of Shanxi Province under Grant 202403021222026.
+
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2025/Disco4D_ Disentangled 4D Human Generation and Animation from a Single Image/5f039bdf-5dd5-496e-b90f-b0a10473c8cd_content_list.json

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+    {
+        "type": "text",
+        "text": "Disco4D: Disentangled 4D Human Generation and Animation from a Single Image",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Hui En Pang $^{1}$ , Shuai Liu $^{3}$ , Zhongang Cai $^{1,2,3}$ , Lei Yang $^{2,3}$ , Tianwei Zhang $^{1}$ , Ziwei Liu $^{1}$",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "$^{1}$ S-Lab, Nanyang Technological University  $^{2}$ SenseTime Research  $^{3}$ Shanghai AI Laboratory",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/95e2c828af253cd8c94fd8208bcc383a17ce69683a910e6599a18759da9fab83.jpg",
+        "image_caption": [
+            "Figure 1. Disco4D is a novel Gaussian Splatting framework for 4D disentangled human generation from a single image. Clothing and assets are modeled as Gaussians on top of the SMPL-X body, enabling dynamic animation and flexible editing."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We present Disco4D, a novel Gaussian Splatting framework for 4D human generation and animation from a single image. Different from existing methods, Disco4D distinctively disentangles clothings (with Gaussian models) from the human body (with SMPL-X model), significantly enhancing the generation details and flexibility. Specifically, 1) Disco4D learns to efficiently fit the clothing Gaussians over the SMPL-X Gaussians. 2) Next, Disco4D adopts diffusion models to enhance the 3D generation process, e.g., modeling occluded parts not visible in the input image. 3) Finally, Disco4D learns an identity encoding for each clothing Gaussian to facilitate the separation and extraction of clothing assets. Furthermore, Disco4D naturally supports 4D human animation with vivid dynamics. Extensive experiments demonstrate the superiority of Disco4D on 4D human generation and animation tasks. Our code is available at https://github.com/disco-4d/Disco4D.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The development of high-fidelity 3D digital humans is increasingly important across a variety of augmented and virtual reality applications. To streamline the creation of these digital avatars from easily accessible in-the-wild images, a multitude of research efforts have been made on reconstructing 3D clothed human models from a single image [2, 33, 40-42, 81, 82, 103, 104, 104, 117]. These works predominantly focus on the simultaneous reconstruction of",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "the human body and clothing. Unfortunately, these works have inherent limitations, and integrating them into applications that require virtual try-on or avatar customization poses significant challenges. This is primarily because the models are rendered as single-layer, non-animatable meshes where distinct attributes (e.g., hair, clothing, accessories) are merged into one continuous surface, with underlying layers completely obscured and self-contact areas inseparably connected. Such limitation complicates the re-animation and dynamic customization tasks. Existing works that perform layered reconstruction [25, 26] rely on self-rotating video inputs with extensive frames and viewpoints and involve substantial processing times.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To address these issues, we propose Disco4D, a novel 4D clothed human reconstruction method that distinctly separates the human body from clothing elements from a single image. It supports human animation as the 4th dimension, which cannot be realized by prior static 3D reconstruction works [2, 33, 42, 81, 82, 103, 104, 117]. To achieve this, it employs the SMPL-X [71] parametric model to represent the human body, capitalizing on its efficacy in capturing body structure and kinematics. Conversely, clothing, along with dynamic and variable elements such as hair and accessories, is represented using Gaussian models, which are able to model the large variability in clothing. By binding Gaussians to a SMPL-X model and fixing it during the training phase, Disco4D ensures the integrity of the body while focusing the learning process on the appearance aspects. To model occluded portions not visible in the input image, diffusion models are used to enhance the 3D generation process. Moreover, Disco4D includes an identity grouping mecha",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "26331",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "nism for the Gaussians, which is instrumental in maintaining the separability and individuality of each clothing asset.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The independent reconstruction of clothing and body offers several advantages. (1) Enhanced reconstruction fidelity. The SMPL-X body serves as a stable anchor for the clothing to conform to. By isolating the focus to learn clothing Gaussians, we achieve a more refined geometry and intricate detailing in the clothed model. (2) Fine-grained categorization and extraction of clothing items. Disco4D is able to separate clothing Gaussians into their respective categories, which is crucial for the recovery and utilization of individual clothing assets. (3) Extensive editing capabilities. Disco4D supports different editing functions, including the removal of specific items, inpainting (altering color or material), and other modifications. Such rich editing options allow for precise adjustments to individual assets without inadvertently affecting adjacent elements. This level of control is particularly beneficial in applications requiring detailed customization, such as virtual fashion design and digital content creation. (4) Improved animation capabilities. The body Gaussians adhere to the deformations dictated by the SMPL-X model, while clothing Gaussians conform to the underlying body movements but also exhibit behaviors true to their material characteristics. The disentangled deformation allows for nuanced adjustments to clothing behavior in response to complex body movements, thereby elevating the quality of clothed human animation.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Table 1 summarizes the relevant 3D/4D generation methods. We describe their details below.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1.3D Generation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Single-image 3D Generation. Single-image reconstruction leverages advanced methods [45, 67] to generate 3D assets in the form of 3D point clouds or NeRF [65] from one image. While earlier efforts using auto-encoders focused on synthetic objects [12, 14, 21, 88, 93, 105], newer approaches treat the task as conditional generation, employing diffusion models [35] for 3D generation from both image and text [19, 35, 60, 64, 74, 76, 79, 90]. One-2-3-45 [59] uses 2D diffusion models [60, 87] to generate multiview images for reconstruction, while LRM [36] adopts transformer-based architecture to scale up the task on large datasets [19, 112]. Gaussian-based methods [47], particularly DreamGaussian [89] and LGM [91], offer efficient, high-resolution 3D model generation from text or images. Recently, video diffusion models have attracted significant attention due to their remarkable ability to generate intricate scenes and complex dynamics with great spatio-temporal consistency [4, 7-9, 31, 56, 116]. They are employed to generate consistent multi-view images, and then reconstruct underlying 3D assets with high quality [15].",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2963fa4e815a0db6e0cb0f849e4b7dc57e671763a5eef8ce332a45006557f049.jpg",
+        "table_caption": [
+            "Table 1. 3D/4D generation methods from a single image."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Type</td><td>Layered</td><td>Animatable</td></tr><tr><td>LGM [91]</td><td>General</td><td>X</td><td>X</td></tr><tr><td>PiFU [81]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>DreamFusion [74]</td><td>General</td><td>X</td><td>X</td></tr><tr><td>DreamGaussian [89]</td><td>General</td><td>X</td><td>X</td></tr><tr><td>PiFU [81]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>D-IF [107]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>HiLo [108]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>ECON [104]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>SHERF [40]</td><td>Human-centric</td><td>X</td><td>✓</td></tr><tr><td>Disco4D</td><td>Human-centric</td><td>✓</td><td>✓</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Single-image human-centric 3D Generation. Significant research efforts have been made for 3D human reconstruction, which can be classified into the following categories. (1) Explicit-shape-based methods rely on Human Mesh Recovery (HMR) using parametric models like SMPL [62] and SMPL-X [71] to generate 3D body meshes [16, 17, 22, 24, 44, 46, 48, 49, 51, 66, 80, 118]. To account for 3D garments, several approaches incorporate offsets [99, 119] or templates, utilize deformable garment templates [6, 43], or employ non-parametric forms for clothed figures [27, 104, 115]. Despite their advancements, they face limitations in handling complex outfit variations and loose clothing due to inherent topological constraints. (2) Implicit-function-based methods utilize implicit representations like occupancy or distance fields for modeling clothed humans with complex geometries, such as loose garments. Techniques range from end-to-end regression of free-form implicit surfaces [2, 81, 82] to use of geometric priors [33, 42, 103, 104, 117] and implicit shape completion [104]. Notable works such as PIFu [81], ARCH(++) [33, 42], and PaMIR [117] can extract textured models from images, but struggle with depth ambiguities and texture inconsistencies. (3) NeRF-based methods incorporate model-based priors (i.e., SMPL-X) for accurate human reconstruction. Efforts like SHERF [40] and ELICIT [41] improve the reconstruction coherence by addressing 2D observation incompleteness leveraging appearance priors. Most of these 3D clothed human reconstruction and animation works [2, 33, 42, 81, 82, 103, 104, 117] require training on human-specific datasets, which brings another limitation on the availability of such datasets.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3D Clothing Modeling. Reconstructing clothing from images and videos as a separate layer over the human body poses significant challenges due to the diversity of clothing topologies. Previous efforts relied on either template meshes or implicit surface models, and required extensive, high-quality 3D data from simulations [5, 70, 83, 95] or tailored template meshes [13, 32, 73, 100]. New methods were developed [34, 43] for multi-clothing models and versatile template meshes, respectively, facilitating diverse clothing topology encoding. However, these techniques typically fall short in capturing the clothing texture and appearance. The reliance on predefined clothing style templates further con",
+        "bbox": [
+            511,
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+            910,
+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "26332",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "strains their ability to handle real-world clothing variations. Corona et al. [18] addressed these shortcomings by representing clothing layers with deep unsigned distance functions and an auto-decoder for style and cut differentiation, though this often produces overly-smooth reconstructions [18]. On the other hand, SCARF [25] and DELTA [26] significantly enhance the visual fidelity by applying NeRF to clothing layers, but require self-rotating video inputs and considerable processing times.",
+        "bbox": [
+            89,
+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. 4D Animation",
+        "text_level": 1,
+        "bbox": [
+            89,
+            246,
+            235,
+            260
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4D Animation. This task aims at capturing dynamic 3D scenes over time. Two primary approaches have emerged: modeling 4D scenes by adding time dimension  $t$  or latent codes to spatial coordinates [28, 57, 98]; combining deformation fields with static 3D scenes [20, 58, 68, 69, 75, 92, 114]. Recent efforts in explicit or hybrid representations, like planar decomposition [11, 84, 85], hash representations [94], and other innovative methods [1, 23, 29], have improved reconstruction speed and quality. Gaussian Splatting, especially, stands out for balancing efficiency with quality, with dynamic 3D Gaussians [63] and 4D Gaussian Splatting [97, 110] techniques introducing time-dependent deformations to enhance reconstructions. Notably, DreamGaussian4D [78] stands out by minimizing the optimization time while achieving high-quality 4D reconstructions.",
+        "bbox": [
+            89,
+            271,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Human-centric 4D Animation. Recent works leverage Gaussian-based methods [38, 50, 54, 55, 61, 77, 113] for 4D human reconstruction, requiring extensive frame sequences (50-100 frames) and/or multiple viewpoints. Currently there has not been any work on 4D layered human generation and animation from a single image or a video with few images, which will be achieved in this paper.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3D Gaussian Splatting employs explicit 3D Gaussian points as its primary rendering entities. A 3D Gaussian point is defined as a function  $G(x) = e^{-\\frac{1}{2}(x - \\mu)^T\\Sigma^{-1}(x - \\mu)}$ , where  $\\mu$  and  $\\Sigma$  are the spatial mean and covariance matrix, respectively. Each Gaussian is also associated with its own rotation  $r$ , scaling  $s$ , opacity  $\\alpha$ , a view-dependent color  $c$  represented by spherical harmonic coefficients  $f$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "SMPL-X parameterization [71] is an extension of the SMPL body model [62] with face and hand, designed to capture a more accurate representation of intricate body movements. SMPL-X is defined as a function  $M(\\beta, \\theta, \\psi) : \\mathbb{R}^{|\\beta| \\times |\\theta| \\times |\\psi|} \\to \\mathbb{R}^{3N}$ , parametrized by the pose  $\\theta \\in \\mathbb{R}^{3J}$  (where  $J$  denotes the number of full body joints), body shape  $\\beta \\in \\mathbb{R}^{|\\beta|}$  and facial expression  $\\psi \\in \\mathbb{R}^{|\\psi|}$ .",
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+    {
+        "type": "text",
+        "text": "3.2. Overview",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a single image, Disco4D generates animatable 3D clothed human avatars in a bottom-up manner, facilitating natural separability. Our generated 3D clothed avatars, denoted as  $S_{human}$ , are represented as the concatenation of  $S_{body}$  and  $S_{cloth}$ . Inspired by prior works [89, 91],  $S$  capitalizes on Gaussian representations:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS = G (\\mu , r, s, \\alpha , c, e), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu, r, s, \\alpha, c$  and  $e$  denote positions, rotation, scaling, opacity, spherical harmonics coefficients and identity encoding, respectively. Different from traditional Gaussian representations, we add identity encoding  $e$  to associate each Gaussian with its clothing category.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Figure 2 depicts our framework. We start by generating colored SMPL-X Gaussians representing the body beneath clothing (Sec. 3.3). We obtain a visual hull for canonicalization and refine Gaussian predictions to align and envelop the SMPL-X mesh (Sec. 3.4). Next, we iteratively optimize canonical clothing Gaussians external to the SMPL-X mesh (Sec. 3.5). Lastly, we showcase the animation and editing of generated clothed avatars (Sec. 3.6). Notably, we leverage diffusion models to refine textures during 3D generation (Sec. 3.5) and extrapolate unseen views during 4D animation (Sec. 3.6).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. SMPL-X Gaussians",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Given an image, we first estimate coarse SMPL-X parameters with an off-the-shelf model [10], and then refine coarse predictions by fitting on 2D keypoints and clothing segmentation masks [72], obtaining pixel-aligned SMPL-X parameters  $(\\beta, \\theta, \\psi)$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Mesh Binding. To convert the SMPL-X [71] mesh  $M(\\beta, \\theta, \\psi)$  into Gaussians  $S_{body}$  for rendering, flat 3D Gaussians are bound to each mesh triangle, similar to SuGaR [30]. Gaussian means  $\\mu_{body}$  are computed using predefined barycentric coordinates, while Gaussian rotations  $r_{body}$  derive from surface normals. The initial scaling  $s_{body}$  ensures dense mesh coverage, with the last axis set to 0.1 for a uniformly thin surface. For color representation beneath clothing, opacity  $\\alpha_{body}$  is set to 1.0, with spherical harmonics  $c_{body}$  optimized for each Gaussian. Visible skin color is supervised, while occluded skin color aligns with visible regions. A fixed label  $e_{body}$  is assigned for rendering, remaining unchanged during training. When optimizing clothing Gaussians  $S_{cloth}$ , SMPL-X Gaussians  $S_{body}$  parameters stay fixed, preserving the body structure while allowing flexible learning for clothing.",
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+        "type": "text",
+        "text": "3.4. Initialization of Clothing Gaussians",
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+        "type": "text",
+        "text": "Cloth styles are diverse, making proper initialization crucial for effective clothing modeling. In synchronization with",
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+    {
+        "type": "image",
+        "img_path": "images/a42620725e9459866868a1c7ce133c3e2b8b35f0d94e5e20c14ece6d76cafb14.jpg",
+        "image_caption": [
+            "Figure 2. Framework Overview of Disco4D. (a) 3D Generation utilizes a single image to obtain disentangled body and clothing Gaussians. Body, face and hand poses are refined to be pixel-aligned. For faster initialization, clothing Gaussians and visual hull are obtained with Gaussian Reconstruction Models. These clothing Gaussians are embedded to SMPL-X mesh and adopt the local coordinate system of the triangle. Subsequently, the iterative optimization process (pruning, identity encoding and densifying) separates the body and garments. The learned identity encodings guide the densification of the clothing Gaussians. (b) 4D Animation is achieved by either direct driving of SMPL-X poses or leveraging video to learn extra clothing deformation (refer to Figure 3 for more details). Various (c) 3D/4D Editing operations can be performed with our disentangled representation."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "estimating SMPL-X, we first employ the Video Diffusion Model [7] to estimate multi-view images. Subsequently, we leverage Gaussian Reconstruction Models [91] to obtain initial 3D Gaussians and their corresponding visual hull. Yet, the reconstructed 3D outputs often suffer from geometric inaccuracies, such as incorrect poses due to pose ambiguity or missing limbs. To address this, we refine the coarse visual hull to ensure it accurately aligns with and overlays the SMPL-X mesh and encapsulates a good geometry for the clothed figure. With SMPL-X aligned visual hull, we derive the refined Gaussians by adopting properties from their nearest neighbors. The refined visual hull and Gaussians are then canonicalized for the optimization phase.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Mesh embedding. Each 3D clothing Gaussian is embedded on a triangle of the canonical mesh, defining its position in both canonical and posed spaces. The mean vertex position  $\\mathbf{O}$  serves as the origin of the local coordinate system, with the Gaussian positioned by an offset vector  $\\mathbf{v} = \\sigma \\mathbf{i} + \\beta \\mathbf{j} + \\gamma \\mathbf{k}$ , where  $\\sigma$ ,  $\\beta$ , and  $\\gamma$  are the components of the displacement vector along the tangent  $\\mathbf{i}$ , bitangent  $\\mathbf{j}$ , and normal  $\\mathbf{k}$ . Unlike SplattingAvatar [86], which displaces Gaussians along the normal, our approach allows embedding to the most suitable triangle rather than the nearest one. For example, hair Gaussians are tagged to head faces instead of the nearest face for reposing [39, 86] (Figure 9 in Appendix). In animation, the Gaussian rotates with its embedded triangle face  $(\\delta r)$ , while scaling  $(\\delta s)$  is adjusted dynamically based on changes in edge lengths. During optimization, Gaussian and embedding parameters  $(\\mathbf{O}, \\mathbf{v}, \\delta r, \\text{and } \\delta s)$  are jointly updated.",
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+    },
+    {
+        "type": "text",
+        "text": "3.5. Optimization of Separable Gaussians",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "With the SMPL-X Gaussian and initialized clothing Gaussian, we aim to optimize canonical clothing Gaussians  $S_{cloth}$",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "outside the SMPL-X mesh. This involves three steps: 1) we use Signed Distance Function (SDF) loss and pruning to discourage and remove Gaussians that reside within the body; 2) we introduce identity encoding  $e$  to attach a clothing label for each clothing Gaussian, by lifting multi-view 2D segmentations of the target object onto the 3D Gaussians; and 3) guided by  $e_{body}$  and  $e_{cloth}$ , we selectively densify only the relevant clothing points while ignoring body points. Once the disentangled clothing is obtained, we use SDS loss to in-paint high-resolution texture from the reference image to individual clothing Gaussians, thereby enriching the details of unseen regions.",
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+    {
+        "type": "text",
+        "text": "SDF Loss and Pruning. In reality, the clothing is always external to the body. During refinement, we ensure that the clothing Gaussians are positioned externally to the SMPL-X mesh by applying the SDF loss and a pruning strategy. Specifically, the SDF loss  $\\mathcal{L}_{sdf}$  penalizes any new densified Gaussians that intrude into the space of the SMPL-X mesh, ensuring that the clothing Gaussians consistently remain outside the body's surface. Pruning is applied at fixed intervals to reinforce this separation, and systematically remove any Gaussians located within the SDF of the SMPL-X mesh.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Identity encoding. To associate each Gaussian to its clothing category, we introduce Identity Encoding  $(e)$ , a learnable and compact vector of length 15, representing clothing categories from SegFormer [101] segmentation masks<sup>1</sup>. During training, the encodings are rendered into 2D segmentation masks in a differentiable manner following [111]. For classification, we apply a softmax to the rendered features  $E_{\\mathrm{id}}$  and use cross-entropy loss  $\\mathcal{L}_{2d}$  for  $(K + 1)$ -category classifica",
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+    {
+        "type": "page_footnote",
+        "text": "1Categories: 0: \"Background\", 1: \"Hat\", 2: \"Hair\", 3: \"Sunglasses\", 4: \"Upper-clothes\", 5: \"Skirt\", 6: \"Pants\", 7: \"Dress\", 8: \"Belt\", 9: \"Left-shoe\", 10: \"Right-shoe\", 11: \"Face\", 12: \"Skin\", 13: \"Bag\", 14: \"Scarf\"",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "26334",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "tion. An unsupervised 3D regularization loss  $\\mathcal{L}_{3d}$  promotes spatial consistency among the top  $k$ -nearest 3D Gaussians' Identity Encodings. Consequently, the overall identity loss is  $\\mathcal{L}_{id} = \\mathcal{L}_{2d} + \\mathcal{L}_{3d}$ . Refer to Appendix 7.2 for more details. Densification of clothing Gaussians. To learn clothing more efficiently, we perform sampling for categorical Gaussians that belong to the same clothing category and embedding. We find the  $k$ -nearest Gaussian points for the resampled points and inherit their Gaussian properties (scaling, rotation, opacity, SH properties). By selectively densifying clothing Gaussians, we only add necessary Gaussians while ignoring body Gaussians.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Anisotropy. To prevent overly-skinny kernels that point outward from the object surface under large deformations, we enforce the anisotropy of Gaussian kernels following [102]. During optimization, we employ  $\\mathcal{L}_{\\mathrm{ani}} = \\frac{1}{|P|}\\sum_{p\\in P}\\max \\left(\\frac{\\max(s_p)}{\\min(s_p)},\\tau\\right) - \\tau$ , where  $s_p$  is the scalings of 3D Gaussians. This loss constrains the ratio between the major and minor axis lengths below threshold  $\\tau$ .",
+        "bbox": [
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+            383
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Total loss. To inpaint occluded textures, we use the  $\\mathcal{L}_{SDS}$  loss on the Gaussians in the canonical pose after optimizing the front view for 500 steps. Combined with the conventional 3D Gaussian Loss  $\\mathcal{L}_{ori}$  on image rendering, the total loss  $L$  for end-to-end optimization of clothing Gaussians via network  $C_N$  is:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\lambda_ {\\text {o r i}} \\mathcal {L} _ {\\text {o r i}} + \\lambda_ {\\text {i d}} \\mathcal {L} _ {\\text {i d}} + \\lambda_ {\\text {a n i}} \\mathcal {L} _ {\\text {a n i}} + \\lambda_ {\\text {s d f}} \\mathcal {L} _ {\\text {s d f}} + \\lambda_ {\\text {S D S}} \\mathcal {L} _ {\\text {S D S}} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.6. 4D Human Animation and Editing",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/0f4a91071a9f36466d5bc8dae4a308e65ce2cab82b34981bcabd105fe8f64912.jpg",
+        "image_caption": [
+            "a) SMPL-X Pose Driven Animation"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            554,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/18159098878650bcb17563218212498802af2f353eefda2c9c7cb61d3d527ddb.jpg",
+        "image_caption": [
+            "b) Video-to-4D Reconstruction",
+            "Figure 3. 4D animation is achieved by (a) driving SMPL-X poses or (b) using video to learn additional clothing deformations. From the first frame, a static 3D disentangled GS model is generated. Pose transformations deform body and clothing Gaussians, and a deformation network is optimized to capture additional clothing deformations over time."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            109,
+            623,
+            467,
+            820
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Disco4D's disentangled representation naturally supports animation and editing. The canonical Gaussians  $S_{body}$  and  $S_{cloth}$  enable separate deformations for clothing and body, ensuring realistic animation. Besides, individual clothing categories can be easily edited using image or text prompts. The learned clothing can be transferred to different body shapes and poses, for versatile customization.",
+        "bbox": [
+            511,
+            90,
+            906,
+            196
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Animating Gaussians. As shown in Figure 2, Disco4D enables animation of the canonical human Gaussian via two methods. Firstly, Gaussians can be directly driven using 3D SMPL-X sequences obtained from a motion database or estimated from 2D videos. Secondly, Disco4D enhances the model by learning detailed clothing dynamics from monocular videos. This disentanglement enables the focused modeling of clothing dynamics without altering the underlying human representation.",
+        "bbox": [
+            511,
+            198,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To extend static 3D Gaussians into dynamic 4D Gaussians, a deformation network is trained to predict changes in position, rotation, and scale of the reposed clothing Gaussians based on a timestamp, as described in DreamGaussian4D [78]. Unlike [78], which learns deformations for all Gaussians, Disco4D models body Gaussians using the SMPL-X mesh, while clothing Gaussians employ posed transformations and learned deformations. The transformation is defined as  $S'' = D_N(S', t)$  where  $D_N$  is the deformation network,  $S'$  is the spatial descriptions of the reposed 3D clothing Gaussian,  $t$  is the timestamp, and  $S''$  is the spatial descriptions of the deformed and reposed 3D clothing Gaussians. Following [78], the deformation model is initialized to predict zero deformation at the start of training to avoid divergence between dynamic and static models. The weights and biases of the final prediction heads are initialized to zero, and skip connections are introduced to enable gradient backpropagation.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To optimize the deformation field using the reference view video, we minimize the reconstruction loss  $\\mathcal{L}_{Ref}$  between the rendered image and video frame at each timestep. To propagate the motion from the reference view to the entire 3D model, we leverage Zero-1-to-3-XL [19] to predict the deformation of the unseen part to calculate  $\\mathcal{L}_{SDS}$ . Despite per-frame predictions of image diffusion models, the fixed color and opacity of static 3D Gaussians help preserve temporal consistency.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Editing Clothing Gaussians. We extract the Gaussians corresponding to the specific category and edit them. This allows fine-grained editing and ensures that other Gaussians are not affected. Instead of fine-tuning all 3D Gaussians, we freeze the properties for most of the well-trained Gaussians and only adjust a small part of 3D Gaussians relevant to the target categories. For 3D object removal, we simply delete the 3D Gaussians of the editing target. For 3D object colorization by in-painting or text guidance, we reinitialize the color and tune the color (SH) parameters of the correspond-",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "26335",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "ing Gaussian group, while fixing the 3D positions and other properties to preserve the learned 3D geometry.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            89,
+            133,
+            225,
+            152
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our detailed implementation and experiment setup can be found in Appendix 7.3.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1.3D Generation",
+        "text_level": 1,
+        "bbox": [
+            89,
+            198,
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+            213
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Generation and Disentanglement. Our generation and disentanglement results are presented in Figure 4 and Table 2. We assessed the disentanglement quality using the Synbody [109] and CloSe [3] datasets, rendering 30 and 110 clothed human meshes respectively from four angles and evaluating CLIP-similarity, PSNR, SSIM, and LPIPS for various poses and views within the CloSe dataset. disco4D leverages diffusion models without requiring training on human specific datasets. Therefore, we compare it with DreamGaussian [89] and LGM [91] which reconstruct 3D objects from diffusion models. Additionally, we conducted comparisons with SHERF, a human-centric baseline for evaluating novel poses and views. Figure 4 shows disco4D has higher fidelity and better geometry for body parts such as face and limbs due to the representation using SMPL-X Gaussians. It outperforms DreamGaussian and SHERF on SynBody and CloSe benchmarks. disco4D performs worse than LGM on novel views, likely due to its optimization of Gaussians in canonical space for pose generalization, compromising view-specific detail. Editing. We can edit specific clothing appearance given an image or text prompt, repose the person and transfer person characteristics. The disentanglement allows fine-grained editing and modification of individual assets without affecting other assets, and stacking multiple edits (Figure 4). User study. We conducted a user study to evaluate the generative quality of our image-to-3D Gaussians reconstruction on random in-the-wild images from SHHQ, detailed in Table 3. This study focuses on reference view consistency and overall generation quality, crucial aspects in image reconstruction tasks. We rendered 360-degree rotation videos for 25 images generated by DreamGaussian, LGM, and disco4D. We invited 43 volunteers to rate  $24\\sim 27$  mixed samples from these methods on image consistency and overall model quality, yielding 1080 valid scores. As shown in Table 3, disco4D was preferred, demonstrating better alignment with the original image content and superior overall quality.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. 4D Animation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Pose-Driven Animation. disco4D generates canonical Gaussians that can be animated with any pose sequence. Figure 12 in the Appendix demonstrates our animation capabilities and compares them with current SOTA 2D animation methods. Using identical inputs—a single frame and pose sequence—our approach more effectively preserves the body shape and fine details such as facial features and clothing. It",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "surpasses Animate-Anyone [37] and Magic-Animate [106] in accurately modeling fine-grained body parts like hands and faces, and exhibits greater consistency compared to CHAMP [120]. The disentanglement feature of Disco4D further allows for direct manipulation of Clothing Gaussians, as shown in Figure 6.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4D Reconstruction. For the 4D-Dress Dataset [96], we evaluated 8 sequences, assessing CLIP similarity scores against ground-truth meshes and disentangled assets, along with novel view performance (PSNR, SSIM, LPIPS) from four viewpoints. Table 4 summarizes our quantitative results, benchmarking Disco4D against existing video-to-4D general GS approaches, such as DreamGaussian4D [78], as well as human-centric GS methods, including MonoHuman [113], GART [54], and GaussianAvatar [38]. We evaluate on monocular videos comprising 14 frames, captured from a limited front-view perspective, without full-body visibility across frames.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Disco4D outperforms MonoHuman [113], GART [54], and GaussianAvatar [38] (Table 4) as these methods reconstruct using known video information, unable to model unseen regions. Consequently, these methods cannot accurately model back views from front-facing videos, leading to artifacts in other perspectives and canonical space (see Figure 5). In contrast, Disco4D first performs reconstruction and subsequently incorporates details, such as clothing deformation, from the input frames, enabling consistent reconstruction even in unseen viewpoints.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "While DreamGaussian4D [78] is capable of modeling back-view information, the details remain coarse. Our results demonstrate that initializing with our model from the first frame (DreamGaussian4D Disco4D-init) significantly outperforms other initialization methods (DreamGaussian4DLGM init, DreamGaussian init) in both fidelity and geometry (Table 4). Nevertheless, without incorporating human priors, DreamGaussian4D [78] still faces challenges, such as missing limbs and difficulty modeling fine details like facial features (see Figure 13 in Appendix).",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Reposing our canonical avatar enables us to align the body and assets accurately with the inferred postures from the source video, yielding high-quality reconstruction of faces, hands, and garments. Our reposed method surpasses DreamGaussian4D in geometry and fidelity by incorporating human priors. However, reposing alone cannot capture clothing dynamics. To address this, our disentangled approach models clothing deformations on the reposed Gaussians, guided by a diffusion model. As demonstrated in Figure 13 and Table 4, this process enhances the accuracy of clothing resemblance to the ground truth. The combination of asset repositioning and learned deformations improves modeling quality, with repositioning handling pose-driven changes and learned deformations simulating dynamic asset movements as observed in the driving video.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "26336",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/f8a529b962d52f736868671611637835ae46b599aa08d4ce47c5180fad51cd45.jpg",
+        "table_caption": [
+            "Table 2. CLIP-embedding loss for generated humans and segmented assets, and performance (PSNR, SSIM, LPIPS) comparisons for novel poses and views on the Synbody and CloSe datasets across DreamGaussian, LGM, SHERF, and Disco4D."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"6\">SynBody</td><td colspan=\"10\">CloSe</td><td></td></tr><tr><td colspan=\"4\">CLIP</td><td colspan=\"3\">Novel View</td><td colspan=\"4\">CLIP</td><td colspan=\"3\">Novel View</td><td colspan=\"2\">Novel Pose</td><td></td></tr><tr><td>All ↑</td><td>Pants ↑</td><td>Shirt ↑</td><td>Shoes ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>All ↑</td><td>Pants ↑</td><td>Shirt ↑</td><td>Shoes ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td></tr><tr><td>DreamGaussian</td><td>0.751</td><td>0.715</td><td>0.710</td><td>0.749</td><td>13.118</td><td>0.883</td><td>0.229</td><td>0.734</td><td>0.693</td><td>0.674</td><td>0.767</td><td>20.08</td><td>0.939</td><td>0.089</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LGM</td><td>0.807</td><td>0.724</td><td>0.747</td><td>0.760</td><td>12.884</td><td>0.876</td><td>0.228</td><td>0.829</td><td>0.727</td><td>0.712</td><td>0.778</td><td>20.50</td><td>0.939</td><td>0.077</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SHERF</td><td>0.766</td><td>0.649</td><td>0.636</td><td>0.714</td><td>15.189</td><td>0.852</td><td>0.189</td><td>0.777</td><td>0.785</td><td>0.729</td><td>0.801</td><td>18.96</td><td>0.912</td><td>0.083</td><td>15.54</td><td>0.844</td><td>0.165</td></tr><tr><td>Disco4D</td><td>0.851</td><td>0.784</td><td>0.753</td><td>0.801</td><td>15.691</td><td>0.848</td><td>0.185</td><td>0.856</td><td>0.858</td><td>0.810</td><td>0.842</td><td>20.10</td><td>0.918</td><td>0.081</td><td>17.96</td><td>0.851</td><td>0.136</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/d4c087aa346e36287966f162e97293bec9476662da2b7b9f9bf420bcef256338.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative comparison of image generation across DreamGaussian, LGM, SHERF, and Disco4D."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/57fd506cb5851f16f4b2827cb1b859baacff518a16203678fe9f75a94c0c5543.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative comparison of 4D generation between DreamGaussian4D, MonoHuman, GART, GaussianAvatar, and Disco4D."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/4b2da948bac6ce9f771e239d3de5f968ccd804fd06c3345ed3cba2c13270a4c0.jpg",
+        "table_caption": [
+            "Table 3. User study rates quality of generated 3D Gaussians from 1-5. The higher the better."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>Image Consistency ↑</td><td>Overall Quality ↑</td></tr><tr><td>DreamGaussian</td><td>2.017</td><td>1.852</td></tr><tr><td>LGM</td><td>2.338</td><td>2.017</td></tr><tr><td>Disco4D</td><td>3.142</td><td>3.037</td></tr></table>",
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+        "type": "table",
+        "img_path": "images/dbfe3cda0184f66b403e6885cc745a30396ef77df4d91d224cddfc6d86550869.jpg",
+        "table_caption": [
+            "Table 4. CLIP-embedding loss for generated humans and segmented assets, and performance (PSNR, SSIM, LPIPS) comparison on 4D-Dress across various video-to-4D methods."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>All ↑</td><td>Assets ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td></tr><tr><td>DreamGaussian4D</td><td>0.784</td><td>0.769</td><td>20.54</td><td>0.93</td><td>0.080</td></tr><tr><td>MonoHuman</td><td>0.762</td><td>0.743</td><td>20.22</td><td>0.92</td><td>0.086</td></tr><tr><td>GART</td><td>0.800</td><td>0.772</td><td>18.81</td><td>0.92</td><td>0.086</td></tr><tr><td>GaussianAvatar</td><td>0.822</td><td>0.768</td><td>20.01</td><td>0.93</td><td>0.069</td></tr><tr><td>DreamGaussian4D (LGM init)</td><td>0.809</td><td>0.795</td><td>19.16</td><td>0.93</td><td>0.086</td></tr><tr><td>DreamGaussian4D (Disco4D init)</td><td>0.870</td><td>0.849</td><td>21.02</td><td>0.93</td><td>0.065</td></tr><tr><td>Disco4D (reposed)</td><td>0.853</td><td>0.774</td><td>23.94</td><td>0.95</td><td>0.049</td></tr><tr><td>Disco4D (reposed)+learned deformations</td><td>0.900</td><td>0.865</td><td>25.46</td><td>0.96</td><td>0.035</td></tr></table>",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/465ac7c73588c24ace8492ee9eb936cb4a42e2d7e2432f4d7178a055f7c44cce.jpg",
+        "image_caption": [
+            "Figure 6. First frame Editing and Animation. Betas Editing, Recoloring (Text/Image-guided), Composition (Removal, Swap)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4D Editing. For a normal pipeline in character animation, editing the person in the video requires high consistency throughout all frames. For pose-driven animation methods, first frame editing and generation is required. Our method directly edits the Gaussians, which is more straightforward, fine-grained and consistent. This is seen from Figure 6.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Initialization of Clothing Gaussians. This process is crucial for high fidelity reconstruction. As shown in Figure 8 in the Appendix, we evaluate different strategies, including random, surface, and hull-based initialization. Hull-based initialization significantly enhances the model accuracy and realism over other methods. Initialization directly on the SMPL-X surface often leads to inaccurate geometries, particularly with complex or loose garments, creating elongated, thin Gaussians and visual artifacts. In contrast, hull-based initialization captures garment details more effectively and maintains pose consistency, closely aligning with the true geometry of the clothed body.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Geometry of Clothing Gaussians. Figure 14 in the Appendix highlights the differences in clothing geometry between DreamGaussian [89], LGM [91] and Disco4D. In",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "DreamGaussian, all points are confined within the body geometry, whereas in LGM, about half of the points extend beyond the SMPL-X body. Removing internal points leaves sparse, translucent representations for clothing. This sparsity suggests reliance on internal points for visual representation, failing to accurately depict the object's geometry where appearance should primarily originate from surface points. Often, clothing Gaussian points are incorrectly positioned inside the body's hull rather than on the surface. To better represent clothing geometry, Disco4D positions all clothing Gaussians externally to the SMPL-X body mesh, accurately reflecting the garment's actual physical characteristics.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Clothing editing. Figure 14 shows our editing results with the prompt \"Color the top pink\". disco4D allows for precise editing of the targeted clothing without affecting other areas.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5. Discussion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Despite achieving impressive results, some failure cases still exist, as shown in Figure 7 in the Appendix. disco4D relies on robust and pixel-aligned SMPL-X estimation, which is still an unsolved problem. It occasionally fails for poor visual hull initialization. The extraction of mesh assets from clothing Gaussians using Local Density Query, as per DreamGaussian [89], currently loses fine-grained details. Enhancing the detail level of geometry derived from clothing Gaussians could bolster the utility of reconstructed assets in animation and simulation applications. Furthermore, the initialized visual hulls obtained from multi-view SMPL-X guided images are often of suboptimal quality and suffer from poor side and back views, necessitating refinement. Improving pose guidance models to achieve more accurate visual hulls could alleviate the need for extensive refinement. In addition, future works could look into modeling multi-layered clothing and reconstructing the occluded clothing. disco4D has many positive applications, but it also has the potential to facilitate deepfake avatars and raise IP concerns. Regulations should be built to address these issues alongside its benefits in the entertainment industry.",
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+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We propose Disco4D, a novel approach for the generation of 3D animatable clothed human Gaussians from a single image, emphasizing high-fidelity detail and separation of assets. We manage to compositionally generate separate components, such as haircut, accessories, and decoupled outfits. Our core insight is the fixing of SMPL-X Gaussians, fitting segmented Gaussians over SMPL-X Gaussians, and application of diffusion models to enhance 3D reconstruction, including modeling occluded parts not visible in the input image. Its capability to separate assets offers significant advantages, including localized, fine-grained editing of individual assets and enhanced animatability.",
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+    },
+    {
+        "type": "page_number",
+        "text": "26338",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We sincerely thank the anonymous reviewers for their valuable comments on this paper. This research/project is supported by the National Research Foundation, Singapore under its AI Singapore Programme(AISG Award No: AISG3-PhD-2023-08-049T). This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012, MOE-T2EP20223-0002), and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
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2025/Disco4D_ Disentangled 4D Human Generation and Animation from a Single Image/5f039bdf-5dd5-496e-b90f-b0a10473c8cd_origin.pdf

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2025/Disco4D_ Disentangled 4D Human Generation and Animation from a Single Image/full.md

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+# Disco4D: Disentangled 4D Human Generation and Animation from a Single Image
+
+Hui En Pang $^{1}$ , Shuai Liu $^{3}$ , Zhongang Cai $^{1,2,3}$ , Lei Yang $^{2,3}$ , Tianwei Zhang $^{1}$ , Ziwei Liu $^{1}$
+
+$^{1}$ S-Lab, Nanyang Technological University  $^{2}$ SenseTime Research  $^{3}$ Shanghai AI Laboratory
+
+![](images/95e2c828af253cd8c94fd8208bcc383a17ce69683a910e6599a18759da9fab83.jpg)  
+Figure 1. Disco4D is a novel Gaussian Splatting framework for 4D disentangled human generation from a single image. Clothing and assets are modeled as Gaussians on top of the SMPL-X body, enabling dynamic animation and flexible editing.
+
+# Abstract
+
+We present Disco4D, a novel Gaussian Splatting framework for 4D human generation and animation from a single image. Different from existing methods, Disco4D distinctively disentangles clothings (with Gaussian models) from the human body (with SMPL-X model), significantly enhancing the generation details and flexibility. Specifically, 1) Disco4D learns to efficiently fit the clothing Gaussians over the SMPL-X Gaussians. 2) Next, Disco4D adopts diffusion models to enhance the 3D generation process, e.g., modeling occluded parts not visible in the input image. 3) Finally, Disco4D learns an identity encoding for each clothing Gaussian to facilitate the separation and extraction of clothing assets. Furthermore, Disco4D naturally supports 4D human animation with vivid dynamics. Extensive experiments demonstrate the superiority of Disco4D on 4D human generation and animation tasks. Our code is available at https://github.com/disco-4d/Disco4D.
+
+# 1. Introduction
+
+The development of high-fidelity 3D digital humans is increasingly important across a variety of augmented and virtual reality applications. To streamline the creation of these digital avatars from easily accessible in-the-wild images, a multitude of research efforts have been made on reconstructing 3D clothed human models from a single image [2, 33, 40-42, 81, 82, 103, 104, 104, 117]. These works predominantly focus on the simultaneous reconstruction of
+
+the human body and clothing. Unfortunately, these works have inherent limitations, and integrating them into applications that require virtual try-on or avatar customization poses significant challenges. This is primarily because the models are rendered as single-layer, non-animatable meshes where distinct attributes (e.g., hair, clothing, accessories) are merged into one continuous surface, with underlying layers completely obscured and self-contact areas inseparably connected. Such limitation complicates the re-animation and dynamic customization tasks. Existing works that perform layered reconstruction [25, 26] rely on self-rotating video inputs with extensive frames and viewpoints and involve substantial processing times.
+
+To address these issues, we propose Disco4D, a novel 4D clothed human reconstruction method that distinctly separates the human body from clothing elements from a single image. It supports human animation as the 4th dimension, which cannot be realized by prior static 3D reconstruction works [2, 33, 42, 81, 82, 103, 104, 117]. To achieve this, it employs the SMPL-X [71] parametric model to represent the human body, capitalizing on its efficacy in capturing body structure and kinematics. Conversely, clothing, along with dynamic and variable elements such as hair and accessories, is represented using Gaussian models, which are able to model the large variability in clothing. By binding Gaussians to a SMPL-X model and fixing it during the training phase, Disco4D ensures the integrity of the body while focusing the learning process on the appearance aspects. To model occluded portions not visible in the input image, diffusion models are used to enhance the 3D generation process. Moreover, Disco4D includes an identity grouping mecha
+
+nism for the Gaussians, which is instrumental in maintaining the separability and individuality of each clothing asset.
+
+The independent reconstruction of clothing and body offers several advantages. (1) Enhanced reconstruction fidelity. The SMPL-X body serves as a stable anchor for the clothing to conform to. By isolating the focus to learn clothing Gaussians, we achieve a more refined geometry and intricate detailing in the clothed model. (2) Fine-grained categorization and extraction of clothing items. Disco4D is able to separate clothing Gaussians into their respective categories, which is crucial for the recovery and utilization of individual clothing assets. (3) Extensive editing capabilities. Disco4D supports different editing functions, including the removal of specific items, inpainting (altering color or material), and other modifications. Such rich editing options allow for precise adjustments to individual assets without inadvertently affecting adjacent elements. This level of control is particularly beneficial in applications requiring detailed customization, such as virtual fashion design and digital content creation. (4) Improved animation capabilities. The body Gaussians adhere to the deformations dictated by the SMPL-X model, while clothing Gaussians conform to the underlying body movements but also exhibit behaviors true to their material characteristics. The disentangled deformation allows for nuanced adjustments to clothing behavior in response to complex body movements, thereby elevating the quality of clothed human animation.
+
+# 2. Related Works
+
+Table 1 summarizes the relevant 3D/4D generation methods. We describe their details below.
+
+# 2.1.3D Generation
+
+Single-image 3D Generation. Single-image reconstruction leverages advanced methods [45, 67] to generate 3D assets in the form of 3D point clouds or NeRF [65] from one image. While earlier efforts using auto-encoders focused on synthetic objects [12, 14, 21, 88, 93, 105], newer approaches treat the task as conditional generation, employing diffusion models [35] for 3D generation from both image and text [19, 35, 60, 64, 74, 76, 79, 90]. One-2-3-45 [59] uses 2D diffusion models [60, 87] to generate multiview images for reconstruction, while LRM [36] adopts transformer-based architecture to scale up the task on large datasets [19, 112]. Gaussian-based methods [47], particularly DreamGaussian [89] and LGM [91], offer efficient, high-resolution 3D model generation from text or images. Recently, video diffusion models have attracted significant attention due to their remarkable ability to generate intricate scenes and complex dynamics with great spatio-temporal consistency [4, 7-9, 31, 56, 116]. They are employed to generate consistent multi-view images, and then reconstruct underlying 3D assets with high quality [15].
+
+Table 1. 3D/4D generation methods from a single image.  
+
+<table><tr><td>Method</td><td>Type</td><td>Layered</td><td>Animatable</td></tr><tr><td>LGM [91]</td><td>General</td><td>X</td><td>X</td></tr><tr><td>PiFU [81]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>DreamFusion [74]</td><td>General</td><td>X</td><td>X</td></tr><tr><td>DreamGaussian [89]</td><td>General</td><td>X</td><td>X</td></tr><tr><td>PiFU [81]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>D-IF [107]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>HiLo [108]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>ECON [104]</td><td>Human-centric</td><td>X</td><td>X</td></tr><tr><td>SHERF [40]</td><td>Human-centric</td><td>X</td><td>✓</td></tr><tr><td>Disco4D</td><td>Human-centric</td><td>✓</td><td>✓</td></tr></table>
+
+Single-image human-centric 3D Generation. Significant research efforts have been made for 3D human reconstruction, which can be classified into the following categories. (1) Explicit-shape-based methods rely on Human Mesh Recovery (HMR) using parametric models like SMPL [62] and SMPL-X [71] to generate 3D body meshes [16, 17, 22, 24, 44, 46, 48, 49, 51, 66, 80, 118]. To account for 3D garments, several approaches incorporate offsets [99, 119] or templates, utilize deformable garment templates [6, 43], or employ non-parametric forms for clothed figures [27, 104, 115]. Despite their advancements, they face limitations in handling complex outfit variations and loose clothing due to inherent topological constraints. (2) Implicit-function-based methods utilize implicit representations like occupancy or distance fields for modeling clothed humans with complex geometries, such as loose garments. Techniques range from end-to-end regression of free-form implicit surfaces [2, 81, 82] to use of geometric priors [33, 42, 103, 104, 117] and implicit shape completion [104]. Notable works such as PIFu [81], ARCH(++) [33, 42], and PaMIR [117] can extract textured models from images, but struggle with depth ambiguities and texture inconsistencies. (3) NeRF-based methods incorporate model-based priors (i.e., SMPL-X) for accurate human reconstruction. Efforts like SHERF [40] and ELICIT [41] improve the reconstruction coherence by addressing 2D observation incompleteness leveraging appearance priors. Most of these 3D clothed human reconstruction and animation works [2, 33, 42, 81, 82, 103, 104, 117] require training on human-specific datasets, which brings another limitation on the availability of such datasets.
+
+3D Clothing Modeling. Reconstructing clothing from images and videos as a separate layer over the human body poses significant challenges due to the diversity of clothing topologies. Previous efforts relied on either template meshes or implicit surface models, and required extensive, high-quality 3D data from simulations [5, 70, 83, 95] or tailored template meshes [13, 32, 73, 100]. New methods were developed [34, 43] for multi-clothing models and versatile template meshes, respectively, facilitating diverse clothing topology encoding. However, these techniques typically fall short in capturing the clothing texture and appearance. The reliance on predefined clothing style templates further con
+
+strains their ability to handle real-world clothing variations. Corona et al. [18] addressed these shortcomings by representing clothing layers with deep unsigned distance functions and an auto-decoder for style and cut differentiation, though this often produces overly-smooth reconstructions [18]. On the other hand, SCARF [25] and DELTA [26] significantly enhance the visual fidelity by applying NeRF to clothing layers, but require self-rotating video inputs and considerable processing times.
+
+# 2.2. 4D Animation
+
+4D Animation. This task aims at capturing dynamic 3D scenes over time. Two primary approaches have emerged: modeling 4D scenes by adding time dimension  $t$  or latent codes to spatial coordinates [28, 57, 98]; combining deformation fields with static 3D scenes [20, 58, 68, 69, 75, 92, 114]. Recent efforts in explicit or hybrid representations, like planar decomposition [11, 84, 85], hash representations [94], and other innovative methods [1, 23, 29], have improved reconstruction speed and quality. Gaussian Splatting, especially, stands out for balancing efficiency with quality, with dynamic 3D Gaussians [63] and 4D Gaussian Splatting [97, 110] techniques introducing time-dependent deformations to enhance reconstructions. Notably, DreamGaussian4D [78] stands out by minimizing the optimization time while achieving high-quality 4D reconstructions.
+
+Human-centric 4D Animation. Recent works leverage Gaussian-based methods [38, 50, 54, 55, 61, 77, 113] for 4D human reconstruction, requiring extensive frame sequences (50-100 frames) and/or multiple viewpoints. Currently there has not been any work on 4D layered human generation and animation from a single image or a video with few images, which will be achieved in this paper.
+
+# 3. Methodology
+
+# 3.1. Preliminaries
+
+3D Gaussian Splatting employs explicit 3D Gaussian points as its primary rendering entities. A 3D Gaussian point is defined as a function  $G(x) = e^{-\frac{1}{2}(x - \mu)^T\Sigma^{-1}(x - \mu)}$ , where  $\mu$  and  $\Sigma$  are the spatial mean and covariance matrix, respectively. Each Gaussian is also associated with its own rotation  $r$ , scaling  $s$ , opacity  $\alpha$ , a view-dependent color  $c$  represented by spherical harmonic coefficients  $f$ .
+
+SMPL-X parameterization [71] is an extension of the SMPL body model [62] with face and hand, designed to capture a more accurate representation of intricate body movements. SMPL-X is defined as a function  $M(\beta, \theta, \psi) : \mathbb{R}^{|\beta| \times |\theta| \times |\psi|} \to \mathbb{R}^{3N}$ , parametrized by the pose  $\theta \in \mathbb{R}^{3J}$  (where  $J$  denotes the number of full body joints), body shape  $\beta \in \mathbb{R}^{|\beta|}$  and facial expression  $\psi \in \mathbb{R}^{|\psi|}$ .
+
+# 3.2. Overview
+
+Given a single image, Disco4D generates animatable 3D clothed human avatars in a bottom-up manner, facilitating natural separability. Our generated 3D clothed avatars, denoted as  $S_{human}$ , are represented as the concatenation of  $S_{body}$  and  $S_{cloth}$ . Inspired by prior works [89, 91],  $S$  capitalizes on Gaussian representations:
+
+$$
+S = G (\mu , r, s, \alpha , c, e), \tag {1}
+$$
+
+where  $\mu, r, s, \alpha, c$  and  $e$  denote positions, rotation, scaling, opacity, spherical harmonics coefficients and identity encoding, respectively. Different from traditional Gaussian representations, we add identity encoding  $e$  to associate each Gaussian with its clothing category.
+
+Figure 2 depicts our framework. We start by generating colored SMPL-X Gaussians representing the body beneath clothing (Sec. 3.3). We obtain a visual hull for canonicalization and refine Gaussian predictions to align and envelop the SMPL-X mesh (Sec. 3.4). Next, we iteratively optimize canonical clothing Gaussians external to the SMPL-X mesh (Sec. 3.5). Lastly, we showcase the animation and editing of generated clothed avatars (Sec. 3.6). Notably, we leverage diffusion models to refine textures during 3D generation (Sec. 3.5) and extrapolate unseen views during 4D animation (Sec. 3.6).
+
+# 3.3. SMPL-X Gaussians
+
+Given an image, we first estimate coarse SMPL-X parameters with an off-the-shelf model [10], and then refine coarse predictions by fitting on 2D keypoints and clothing segmentation masks [72], obtaining pixel-aligned SMPL-X parameters  $(\beta, \theta, \psi)$ .
+
+Mesh Binding. To convert the SMPL-X [71] mesh  $M(\beta, \theta, \psi)$  into Gaussians  $S_{body}$  for rendering, flat 3D Gaussians are bound to each mesh triangle, similar to SuGaR [30]. Gaussian means  $\mu_{body}$  are computed using predefined barycentric coordinates, while Gaussian rotations  $r_{body}$  derive from surface normals. The initial scaling  $s_{body}$  ensures dense mesh coverage, with the last axis set to 0.1 for a uniformly thin surface. For color representation beneath clothing, opacity  $\alpha_{body}$  is set to 1.0, with spherical harmonics  $c_{body}$  optimized for each Gaussian. Visible skin color is supervised, while occluded skin color aligns with visible regions. A fixed label  $e_{body}$  is assigned for rendering, remaining unchanged during training. When optimizing clothing Gaussians  $S_{cloth}$ , SMPL-X Gaussians  $S_{body}$  parameters stay fixed, preserving the body structure while allowing flexible learning for clothing.
+
+# 3.4. Initialization of Clothing Gaussians
+
+Cloth styles are diverse, making proper initialization crucial for effective clothing modeling. In synchronization with
+
+![](images/a42620725e9459866868a1c7ce133c3e2b8b35f0d94e5e20c14ece6d76cafb14.jpg)  
+Figure 2. Framework Overview of Disco4D. (a) 3D Generation utilizes a single image to obtain disentangled body and clothing Gaussians. Body, face and hand poses are refined to be pixel-aligned. For faster initialization, clothing Gaussians and visual hull are obtained with Gaussian Reconstruction Models. These clothing Gaussians are embedded to SMPL-X mesh and adopt the local coordinate system of the triangle. Subsequently, the iterative optimization process (pruning, identity encoding and densifying) separates the body and garments. The learned identity encodings guide the densification of the clothing Gaussians. (b) 4D Animation is achieved by either direct driving of SMPL-X poses or leveraging video to learn extra clothing deformation (refer to Figure 3 for more details). Various (c) 3D/4D Editing operations can be performed with our disentangled representation.
+
+estimating SMPL-X, we first employ the Video Diffusion Model [7] to estimate multi-view images. Subsequently, we leverage Gaussian Reconstruction Models [91] to obtain initial 3D Gaussians and their corresponding visual hull. Yet, the reconstructed 3D outputs often suffer from geometric inaccuracies, such as incorrect poses due to pose ambiguity or missing limbs. To address this, we refine the coarse visual hull to ensure it accurately aligns with and overlays the SMPL-X mesh and encapsulates a good geometry for the clothed figure. With SMPL-X aligned visual hull, we derive the refined Gaussians by adopting properties from their nearest neighbors. The refined visual hull and Gaussians are then canonicalized for the optimization phase.
+
+Mesh embedding. Each 3D clothing Gaussian is embedded on a triangle of the canonical mesh, defining its position in both canonical and posed spaces. The mean vertex position  $\mathbf{O}$  serves as the origin of the local coordinate system, with the Gaussian positioned by an offset vector  $\mathbf{v} = \sigma \mathbf{i} + \beta \mathbf{j} + \gamma \mathbf{k}$ , where  $\sigma$ ,  $\beta$ , and  $\gamma$  are the components of the displacement vector along the tangent  $\mathbf{i}$ , bitangent  $\mathbf{j}$ , and normal  $\mathbf{k}$ . Unlike SplattingAvatar [86], which displaces Gaussians along the normal, our approach allows embedding to the most suitable triangle rather than the nearest one. For example, hair Gaussians are tagged to head faces instead of the nearest face for reposing [39, 86] (Figure 9 in Appendix). In animation, the Gaussian rotates with its embedded triangle face  $(\delta r)$ , while scaling  $(\delta s)$  is adjusted dynamically based on changes in edge lengths. During optimization, Gaussian and embedding parameters  $(\mathbf{O}, \mathbf{v}, \delta r, \text{and } \delta s)$  are jointly updated.
+
+# 3.5. Optimization of Separable Gaussians
+
+With the SMPL-X Gaussian and initialized clothing Gaussian, we aim to optimize canonical clothing Gaussians  $S_{cloth}$
+
+outside the SMPL-X mesh. This involves three steps: 1) we use Signed Distance Function (SDF) loss and pruning to discourage and remove Gaussians that reside within the body; 2) we introduce identity encoding  $e$  to attach a clothing label for each clothing Gaussian, by lifting multi-view 2D segmentations of the target object onto the 3D Gaussians; and 3) guided by  $e_{body}$  and  $e_{cloth}$ , we selectively densify only the relevant clothing points while ignoring body points. Once the disentangled clothing is obtained, we use SDS loss to in-paint high-resolution texture from the reference image to individual clothing Gaussians, thereby enriching the details of unseen regions.
+
+SDF Loss and Pruning. In reality, the clothing is always external to the body. During refinement, we ensure that the clothing Gaussians are positioned externally to the SMPL-X mesh by applying the SDF loss and a pruning strategy. Specifically, the SDF loss  $\mathcal{L}_{sdf}$  penalizes any new densified Gaussians that intrude into the space of the SMPL-X mesh, ensuring that the clothing Gaussians consistently remain outside the body's surface. Pruning is applied at fixed intervals to reinforce this separation, and systematically remove any Gaussians located within the SDF of the SMPL-X mesh.
+
+Identity encoding. To associate each Gaussian to its clothing category, we introduce Identity Encoding  $(e)$ , a learnable and compact vector of length 15, representing clothing categories from SegFormer [101] segmentation masks<sup>1</sup>. During training, the encodings are rendered into 2D segmentation masks in a differentiable manner following [111]. For classification, we apply a softmax to the rendered features  $E_{\mathrm{id}}$  and use cross-entropy loss  $\mathcal{L}_{2d}$  for  $(K + 1)$ -category classifica
+
+tion. An unsupervised 3D regularization loss  $\mathcal{L}_{3d}$  promotes spatial consistency among the top  $k$ -nearest 3D Gaussians' Identity Encodings. Consequently, the overall identity loss is  $\mathcal{L}_{id} = \mathcal{L}_{2d} + \mathcal{L}_{3d}$ . Refer to Appendix 7.2 for more details. Densification of clothing Gaussians. To learn clothing more efficiently, we perform sampling for categorical Gaussians that belong to the same clothing category and embedding. We find the  $k$ -nearest Gaussian points for the resampled points and inherit their Gaussian properties (scaling, rotation, opacity, SH properties). By selectively densifying clothing Gaussians, we only add necessary Gaussians while ignoring body Gaussians.
+
+Anisotropy. To prevent overly-skinny kernels that point outward from the object surface under large deformations, we enforce the anisotropy of Gaussian kernels following [102]. During optimization, we employ  $\mathcal{L}_{\mathrm{ani}} = \frac{1}{|P|}\sum_{p\in P}\max \left(\frac{\max(s_p)}{\min(s_p)},\tau\right) - \tau$ , where  $s_p$  is the scalings of 3D Gaussians. This loss constrains the ratio between the major and minor axis lengths below threshold  $\tau$ .
+
+Total loss. To inpaint occluded textures, we use the  $\mathcal{L}_{SDS}$  loss on the Gaussians in the canonical pose after optimizing the front view for 500 steps. Combined with the conventional 3D Gaussian Loss  $\mathcal{L}_{ori}$  on image rendering, the total loss  $L$  for end-to-end optimization of clothing Gaussians via network  $C_N$  is:
+
+$$
+\mathcal {L} = \lambda_ {\text {o r i}} \mathcal {L} _ {\text {o r i}} + \lambda_ {\text {i d}} \mathcal {L} _ {\text {i d}} + \lambda_ {\text {a n i}} \mathcal {L} _ {\text {a n i}} + \lambda_ {\text {s d f}} \mathcal {L} _ {\text {s d f}} + \lambda_ {\text {S D S}} \mathcal {L} _ {\text {S D S}} \tag {2}
+$$
+
+# 3.6. 4D Human Animation and Editing
+
+![](images/0f4a91071a9f36466d5bc8dae4a308e65ce2cab82b34981bcabd105fe8f64912.jpg)  
+a) SMPL-X Pose Driven Animation
+
+![](images/18159098878650bcb17563218212498802af2f353eefda2c9c7cb61d3d527ddb.jpg)  
+b) Video-to-4D Reconstruction  
+Figure 3. 4D animation is achieved by (a) driving SMPL-X poses or (b) using video to learn additional clothing deformations. From the first frame, a static 3D disentangled GS model is generated. Pose transformations deform body and clothing Gaussians, and a deformation network is optimized to capture additional clothing deformations over time.
+
+Disco4D's disentangled representation naturally supports animation and editing. The canonical Gaussians  $S_{body}$  and  $S_{cloth}$  enable separate deformations for clothing and body, ensuring realistic animation. Besides, individual clothing categories can be easily edited using image or text prompts. The learned clothing can be transferred to different body shapes and poses, for versatile customization.
+
+Animating Gaussians. As shown in Figure 2, Disco4D enables animation of the canonical human Gaussian via two methods. Firstly, Gaussians can be directly driven using 3D SMPL-X sequences obtained from a motion database or estimated from 2D videos. Secondly, Disco4D enhances the model by learning detailed clothing dynamics from monocular videos. This disentanglement enables the focused modeling of clothing dynamics without altering the underlying human representation.
+
+To extend static 3D Gaussians into dynamic 4D Gaussians, a deformation network is trained to predict changes in position, rotation, and scale of the reposed clothing Gaussians based on a timestamp, as described in DreamGaussian4D [78]. Unlike [78], which learns deformations for all Gaussians, Disco4D models body Gaussians using the SMPL-X mesh, while clothing Gaussians employ posed transformations and learned deformations. The transformation is defined as  $S'' = D_N(S', t)$  where  $D_N$  is the deformation network,  $S'$  is the spatial descriptions of the reposed 3D clothing Gaussian,  $t$  is the timestamp, and  $S''$  is the spatial descriptions of the deformed and reposed 3D clothing Gaussians. Following [78], the deformation model is initialized to predict zero deformation at the start of training to avoid divergence between dynamic and static models. The weights and biases of the final prediction heads are initialized to zero, and skip connections are introduced to enable gradient backpropagation.
+
+To optimize the deformation field using the reference view video, we minimize the reconstruction loss  $\mathcal{L}_{Ref}$  between the rendered image and video frame at each timestep. To propagate the motion from the reference view to the entire 3D model, we leverage Zero-1-to-3-XL [19] to predict the deformation of the unseen part to calculate  $\mathcal{L}_{SDS}$ . Despite per-frame predictions of image diffusion models, the fixed color and opacity of static 3D Gaussians help preserve temporal consistency.
+
+Editing Clothing Gaussians. We extract the Gaussians corresponding to the specific category and edit them. This allows fine-grained editing and ensures that other Gaussians are not affected. Instead of fine-tuning all 3D Gaussians, we freeze the properties for most of the well-trained Gaussians and only adjust a small part of 3D Gaussians relevant to the target categories. For 3D object removal, we simply delete the 3D Gaussians of the editing target. For 3D object colorization by in-painting or text guidance, we reinitialize the color and tune the color (SH) parameters of the correspond-
+
+ing Gaussian group, while fixing the 3D positions and other properties to preserve the learned 3D geometry.
+
+# 4. Experiments
+
+Our detailed implementation and experiment setup can be found in Appendix 7.3.
+
+# 4.1.3D Generation
+
+Generation and Disentanglement. Our generation and disentanglement results are presented in Figure 4 and Table 2. We assessed the disentanglement quality using the Synbody [109] and CloSe [3] datasets, rendering 30 and 110 clothed human meshes respectively from four angles and evaluating CLIP-similarity, PSNR, SSIM, and LPIPS for various poses and views within the CloSe dataset. disco4D leverages diffusion models without requiring training on human specific datasets. Therefore, we compare it with DreamGaussian [89] and LGM [91] which reconstruct 3D objects from diffusion models. Additionally, we conducted comparisons with SHERF, a human-centric baseline for evaluating novel poses and views. Figure 4 shows disco4D has higher fidelity and better geometry for body parts such as face and limbs due to the representation using SMPL-X Gaussians. It outperforms DreamGaussian and SHERF on SynBody and CloSe benchmarks. disco4D performs worse than LGM on novel views, likely due to its optimization of Gaussians in canonical space for pose generalization, compromising view-specific detail. Editing. We can edit specific clothing appearance given an image or text prompt, repose the person and transfer person characteristics. The disentanglement allows fine-grained editing and modification of individual assets without affecting other assets, and stacking multiple edits (Figure 4). User study. We conducted a user study to evaluate the generative quality of our image-to-3D Gaussians reconstruction on random in-the-wild images from SHHQ, detailed in Table 3. This study focuses on reference view consistency and overall generation quality, crucial aspects in image reconstruction tasks. We rendered 360-degree rotation videos for 25 images generated by DreamGaussian, LGM, and disco4D. We invited 43 volunteers to rate  $24\sim 27$  mixed samples from these methods on image consistency and overall model quality, yielding 1080 valid scores. As shown in Table 3, disco4D was preferred, demonstrating better alignment with the original image content and superior overall quality.
+
+# 4.2. 4D Animation
+
+Pose-Driven Animation. disco4D generates canonical Gaussians that can be animated with any pose sequence. Figure 12 in the Appendix demonstrates our animation capabilities and compares them with current SOTA 2D animation methods. Using identical inputs—a single frame and pose sequence—our approach more effectively preserves the body shape and fine details such as facial features and clothing. It
+
+surpasses Animate-Anyone [37] and Magic-Animate [106] in accurately modeling fine-grained body parts like hands and faces, and exhibits greater consistency compared to CHAMP [120]. The disentanglement feature of Disco4D further allows for direct manipulation of Clothing Gaussians, as shown in Figure 6.
+
+4D Reconstruction. For the 4D-Dress Dataset [96], we evaluated 8 sequences, assessing CLIP similarity scores against ground-truth meshes and disentangled assets, along with novel view performance (PSNR, SSIM, LPIPS) from four viewpoints. Table 4 summarizes our quantitative results, benchmarking Disco4D against existing video-to-4D general GS approaches, such as DreamGaussian4D [78], as well as human-centric GS methods, including MonoHuman [113], GART [54], and GaussianAvatar [38]. We evaluate on monocular videos comprising 14 frames, captured from a limited front-view perspective, without full-body visibility across frames.
+
+Disco4D outperforms MonoHuman [113], GART [54], and GaussianAvatar [38] (Table 4) as these methods reconstruct using known video information, unable to model unseen regions. Consequently, these methods cannot accurately model back views from front-facing videos, leading to artifacts in other perspectives and canonical space (see Figure 5). In contrast, Disco4D first performs reconstruction and subsequently incorporates details, such as clothing deformation, from the input frames, enabling consistent reconstruction even in unseen viewpoints.
+
+While DreamGaussian4D [78] is capable of modeling back-view information, the details remain coarse. Our results demonstrate that initializing with our model from the first frame (DreamGaussian4D Disco4D-init) significantly outperforms other initialization methods (DreamGaussian4DLGM init, DreamGaussian init) in both fidelity and geometry (Table 4). Nevertheless, without incorporating human priors, DreamGaussian4D [78] still faces challenges, such as missing limbs and difficulty modeling fine details like facial features (see Figure 13 in Appendix).
+
+Reposing our canonical avatar enables us to align the body and assets accurately with the inferred postures from the source video, yielding high-quality reconstruction of faces, hands, and garments. Our reposed method surpasses DreamGaussian4D in geometry and fidelity by incorporating human priors. However, reposing alone cannot capture clothing dynamics. To address this, our disentangled approach models clothing deformations on the reposed Gaussians, guided by a diffusion model. As demonstrated in Figure 13 and Table 4, this process enhances the accuracy of clothing resemblance to the ground truth. The combination of asset repositioning and learned deformations improves modeling quality, with repositioning handling pose-driven changes and learned deformations simulating dynamic asset movements as observed in the driving video.
+
+Table 2. CLIP-embedding loss for generated humans and segmented assets, and performance (PSNR, SSIM, LPIPS) comparisons for novel poses and views on the Synbody and CloSe datasets across DreamGaussian, LGM, SHERF, and Disco4D.  
+
+<table><tr><td rowspan="3">Method</td><td colspan="6">SynBody</td><td colspan="10">CloSe</td><td></td></tr><tr><td colspan="4">CLIP</td><td colspan="3">Novel View</td><td colspan="4">CLIP</td><td colspan="3">Novel View</td><td colspan="2">Novel Pose</td><td></td></tr><tr><td>All ↑</td><td>Pants ↑</td><td>Shirt ↑</td><td>Shoes ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>All ↑</td><td>Pants ↑</td><td>Shirt ↑</td><td>Shoes ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td></tr><tr><td>DreamGaussian</td><td>0.751</td><td>0.715</td><td>0.710</td><td>0.749</td><td>13.118</td><td>0.883</td><td>0.229</td><td>0.734</td><td>0.693</td><td>0.674</td><td>0.767</td><td>20.08</td><td>0.939</td><td>0.089</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LGM</td><td>0.807</td><td>0.724</td><td>0.747</td><td>0.760</td><td>12.884</td><td>0.876</td><td>0.228</td><td>0.829</td><td>0.727</td><td>0.712</td><td>0.778</td><td>20.50</td><td>0.939</td><td>0.077</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SHERF</td><td>0.766</td><td>0.649</td><td>0.636</td><td>0.714</td><td>15.189</td><td>0.852</td><td>0.189</td><td>0.777</td><td>0.785</td><td>0.729</td><td>0.801</td><td>18.96</td><td>0.912</td><td>0.083</td><td>15.54</td><td>0.844</td><td>0.165</td></tr><tr><td>Disco4D</td><td>0.851</td><td>0.784</td><td>0.753</td><td>0.801</td><td>15.691</td><td>0.848</td><td>0.185</td><td>0.856</td><td>0.858</td><td>0.810</td><td>0.842</td><td>20.10</td><td>0.918</td><td>0.081</td><td>17.96</td><td>0.851</td><td>0.136</td></tr></table>
+
+![](images/d4c087aa346e36287966f162e97293bec9476662da2b7b9f9bf420bcef256338.jpg)  
+Figure 4. Qualitative comparison of image generation across DreamGaussian, LGM, SHERF, and Disco4D.
+
+![](images/57fd506cb5851f16f4b2827cb1b859baacff518a16203678fe9f75a94c0c5543.jpg)  
+Figure 5. Qualitative comparison of 4D generation between DreamGaussian4D, MonoHuman, GART, GaussianAvatar, and Disco4D.
+
+Table 3. User study rates quality of generated 3D Gaussians from 1-5. The higher the better.  
+
+<table><tr><td>Metric</td><td>Image Consistency ↑</td><td>Overall Quality ↑</td></tr><tr><td>DreamGaussian</td><td>2.017</td><td>1.852</td></tr><tr><td>LGM</td><td>2.338</td><td>2.017</td></tr><tr><td>Disco4D</td><td>3.142</td><td>3.037</td></tr></table>
+
+Table 4. CLIP-embedding loss for generated humans and segmented assets, and performance (PSNR, SSIM, LPIPS) comparison on 4D-Dress across various video-to-4D methods.  
+
+<table><tr><td></td><td>All ↑</td><td>Assets ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td></tr><tr><td>DreamGaussian4D</td><td>0.784</td><td>0.769</td><td>20.54</td><td>0.93</td><td>0.080</td></tr><tr><td>MonoHuman</td><td>0.762</td><td>0.743</td><td>20.22</td><td>0.92</td><td>0.086</td></tr><tr><td>GART</td><td>0.800</td><td>0.772</td><td>18.81</td><td>0.92</td><td>0.086</td></tr><tr><td>GaussianAvatar</td><td>0.822</td><td>0.768</td><td>20.01</td><td>0.93</td><td>0.069</td></tr><tr><td>DreamGaussian4D (LGM init)</td><td>0.809</td><td>0.795</td><td>19.16</td><td>0.93</td><td>0.086</td></tr><tr><td>DreamGaussian4D (Disco4D init)</td><td>0.870</td><td>0.849</td><td>21.02</td><td>0.93</td><td>0.065</td></tr><tr><td>Disco4D (reposed)</td><td>0.853</td><td>0.774</td><td>23.94</td><td>0.95</td><td>0.049</td></tr><tr><td>Disco4D (reposed)+learned deformations</td><td>0.900</td><td>0.865</td><td>25.46</td><td>0.96</td><td>0.035</td></tr></table>
+
+![](images/465ac7c73588c24ace8492ee9eb936cb4a42e2d7e2432f4d7178a055f7c44cce.jpg)  
+Figure 6. First frame Editing and Animation. Betas Editing, Recoloring (Text/Image-guided), Composition (Removal, Swap).
+
+4D Editing. For a normal pipeline in character animation, editing the person in the video requires high consistency throughout all frames. For pose-driven animation methods, first frame editing and generation is required. Our method directly edits the Gaussians, which is more straightforward, fine-grained and consistent. This is seen from Figure 6.
+
+# 4.3. Ablation Studies
+
+Initialization of Clothing Gaussians. This process is crucial for high fidelity reconstruction. As shown in Figure 8 in the Appendix, we evaluate different strategies, including random, surface, and hull-based initialization. Hull-based initialization significantly enhances the model accuracy and realism over other methods. Initialization directly on the SMPL-X surface often leads to inaccurate geometries, particularly with complex or loose garments, creating elongated, thin Gaussians and visual artifacts. In contrast, hull-based initialization captures garment details more effectively and maintains pose consistency, closely aligning with the true geometry of the clothed body.
+
+Geometry of Clothing Gaussians. Figure 14 in the Appendix highlights the differences in clothing geometry between DreamGaussian [89], LGM [91] and Disco4D. In
+
+DreamGaussian, all points are confined within the body geometry, whereas in LGM, about half of the points extend beyond the SMPL-X body. Removing internal points leaves sparse, translucent representations for clothing. This sparsity suggests reliance on internal points for visual representation, failing to accurately depict the object's geometry where appearance should primarily originate from surface points. Often, clothing Gaussian points are incorrectly positioned inside the body's hull rather than on the surface. To better represent clothing geometry, Disco4D positions all clothing Gaussians externally to the SMPL-X body mesh, accurately reflecting the garment's actual physical characteristics.
+
+Clothing editing. Figure 14 shows our editing results with the prompt "Color the top pink". disco4D allows for precise editing of the targeted clothing without affecting other areas.
+
+# 5. Discussion
+
+Despite achieving impressive results, some failure cases still exist, as shown in Figure 7 in the Appendix. disco4D relies on robust and pixel-aligned SMPL-X estimation, which is still an unsolved problem. It occasionally fails for poor visual hull initialization. The extraction of mesh assets from clothing Gaussians using Local Density Query, as per DreamGaussian [89], currently loses fine-grained details. Enhancing the detail level of geometry derived from clothing Gaussians could bolster the utility of reconstructed assets in animation and simulation applications. Furthermore, the initialized visual hulls obtained from multi-view SMPL-X guided images are often of suboptimal quality and suffer from poor side and back views, necessitating refinement. Improving pose guidance models to achieve more accurate visual hulls could alleviate the need for extensive refinement. In addition, future works could look into modeling multi-layered clothing and reconstructing the occluded clothing. disco4D has many positive applications, but it also has the potential to facilitate deepfake avatars and raise IP concerns. Regulations should be built to address these issues alongside its benefits in the entertainment industry.
+
+# 6. Conclusion
+
+We propose Disco4D, a novel approach for the generation of 3D animatable clothed human Gaussians from a single image, emphasizing high-fidelity detail and separation of assets. We manage to compositionally generate separate components, such as haircut, accessories, and decoupled outfits. Our core insight is the fixing of SMPL-X Gaussians, fitting segmented Gaussians over SMPL-X Gaussians, and application of diffusion models to enhance 3D reconstruction, including modeling occluded parts not visible in the input image. Its capability to separate assets offers significant advantages, including localized, fine-grained editing of individual assets and enhanced animatability.
+
+# Acknowledgements
+
+We sincerely thank the anonymous reviewers for their valuable comments on this paper. This research/project is supported by the National Research Foundation, Singapore under its AI Singapore Programme(AISG Award No: AISG3-PhD-2023-08-049T). This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012, MOE-T2EP20223-0002), and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).
+
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+    {
+        "type": "text",
+        "text": "DiscoVLA: Discrepancy Reduction in Vision, Language, and Alignment for Parameter-Efficient Video-Text Retrieval",
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+        "text": "Leqi Shen $^{1,2,4*}$  Guoqiang Gong $^{5\\dagger}$  Tianxiang Hao $^{1,2}$  Tao He $^{6,7}$  Yifeng Zhang $^{5}$  Pengzhang Liu $^{5}$  Sicheng Zhao $^{2‡}$  Jungong Han $^{3}$  Guiguang Ding $^{1,2‡}$",
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+    {
+        "type": "text",
+        "text": "$^{1}$  School of Software  $^{2}$  BNrist  $^{3}$  Department of Automation, Tsinghua University  $^{4}$  Hangzhou Zhuoxi Institute of Brain and Intelligence",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "$^{5}$  JD.com  $^{6}$  GRG Banking Equipment Co., Ltd.  $^{7}$  South China University of Technology",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The parameter-efficient adaptation of the image-text pretraining model CLIP for video-text retrieval is a prominent area of research. While CLIP is focused on image-level vision-language matching, video-text retrieval demands comprehensive understanding at the video level. Three key discrepancies emerge in the transfer from image-level to video-level: vision, language, and alignment. However, existing methods mainly focus on vision while neglecting language and alignment. In this paper, we propose Discrepancy Reduction in Vision, Language, and Alignment (DiscoVLA), which simultaneously mitigates all three discrepancies. Specifically, we introduce Image-Video Features Fusion to integrate image-level and video-level features, effectively tackling both vision and language discrepancies. Additionally, we generate pseudo image captions to learn fine-grained image-level alignment. To mitigate alignment discrepancies, we propose Image-to-Video Alignment Distillation, which leverages image-level alignment knowledge to enhance video-level alignment. Extensive experiments demonstrate the superiority of our DiscoVLA. In particular, on MSRVTT with CLIP (ViT-B/16), DiscoVLA outperforms previous methods by  $2.2\\%$  R@1 and  $7.5\\%$  R@sum. The code is available at https://github.com/LunarShen/DsicoVLA.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "The rapid expansion of online video content has generated a growing demand for effective video-text retrieval, focusing on matching video content with relevant textual descriptions. Inspired by the success of image-text pretraining approaches such as CLIP [42], recent efforts [9, 14, 24, 37, 48, 49, 51] have increasingly focused on extend",
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+    {
+        "type": "image",
+        "img_path": "images/bfbe10255f720db020eda19693dec725fa3660b25e37918a8c85685474458566.jpg",
+        "image_caption": [
+            "Figure 1. When parameter-efficient transferring image-level CLIP to video-text retrieval, we identify three key discrepancies: vision, alignment, and language. Unlike previous methods, our DiscoVLA aims to address all these discrepancies. More visualization examples are provided in Figure 4."
+        ],
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+        "table_caption": [],
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+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">Image-Level PETL Video-Level</td></tr><tr><td>Vision</td><td>Language</td><td>Alignment</td></tr><tr><td>Previous Methods</td><td>✓</td><td>×</td><td>×</td></tr><tr><td>Our DiscoVLA</td><td>✓</td><td>✓</td><td>✓</td></tr></table>",
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+        "text": "ing these powerful capabilities to video-text retrieval tasks. However, fully fine-tuning these pretrained models requires updating numerous parameters for every dataset, resulting in large storage overhead [22, 58]. Therefore, we focus on parameter-efficient transfer learning methods, targeting strong performance with minimal trainable parameters.",
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+        "type": "text",
+        "text": "Although both image-text pretraining and video-text retrieval involve vision-language (VL) matching, they exhibit",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "* lunarshen@gmail.com. Work done during an internship at JD.com.",
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+    {
+        "type": "page_footnote",
+        "text": "†Project leader. ‡ Corresponding authors.",
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+    },
+    {
+        "type": "page_number",
+        "text": "19702",
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+    {
+        "type": "text",
+        "text": "substantial discrepancies that hinder straightforward knowledge transfer. To be specific, image-text pretraining focuses on matching images with image captions, which represents image-level VL matching. In contrast, video-text retrieval focuses on matching videos with video captions, which represents video-level VL matching. The challenges of video-level VL matching, which demands understanding motion and time, create significant obstacles for transferring knowledge from image-text to video-text tasks.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we explore the discrepancies between image-level and video-level VL matching across three key aspects: vision, language, and alignment. Videos introduce a temporal dimension, which is absent in images. Similarly, the distinction between image captions and video captions arises from the varying levels of granularity, such as isolated image descriptions versus continuous video narratives. Thus, video-level alignment is inherently more complex than image-level alignment, as it must account for intricate spatio-temporal relationships. In Figure 1, the three images correspond to \"preparing food\", \"pouring\", and \"cutting\", while the entire video demonstrates an instructional cooking process. Image-level VL matching focuses on isolated images, while video-level VL matching emphasizes the overall understanding of continuous segments.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "However, current methods [5, 22, 25, 58] struggle to fully address the discrepancies mentioned above. Some [5, 22, 25, 58] focus on the vision aspect, modeling temporal relationships to extract video-level features, while others [25, 58] attempt to reduce the modality gap between vision and language through shared parameter mechanisms. Despite these advances, these methods remain limited in both language and alignment discrepancies.",
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+    {
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+        "text": "To tackle these challenges, we introduce Discrepancy Reduction in Vision, Language, and Alignment, termed DiscoVLA, a novel parameter-efficient method for videotext retrieval. Unlike previous methods that target a single gap, our method aims to simultaneously reduce all significant discrepancies, as illustrated in the table of Figure 1.",
+        "bbox": [
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+        "text": "Specifically, we propose an Image-Video Features Fusion module (IVFusion), which addresses both vision and language discrepancies through a unified feature extraction approach. IVFusion effectively combines both image- and video-level features by utilizing a lightweight adapter. In addition to video-level alignment, we propose Pseudo Image-level Alignment (PIImgAlign) which generates pseudo image captions and learns fine-grained image-level alignment. Furthermore, to reduce alignment discrepancy, we propose Image-to-Video Alignment Distillation (AlignDistill), transferring image-level alignment knowledge to improve video-level alignment. All proposed modules prioritize parameter efficiency: IVFusion requires minimal trainable parameters, while PImgAlign and AlignDistill operate without increasing inference parameters.",
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+        "type": "text",
+        "text": "In summary, the main contributions are as follows:",
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+    {
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+        "list_items": [
+            "- We reveal, for the first time, the necessity of addressing all three image-to-video discrepancies—vision, language, and alignment—to achieve parameter-efficient VTR.",
+            "- We introduce IVFusion to fuse image- and video-level features for both vision and language gaps. PImgAlign is introduced for fine-grained image-level alignment. We introduce AlignDistill to minimize alignment gaps.",
+            "- Our DiscoVLA achieves state-of-the-art results on MSRVTT, LSMDC, ActivityNet, and DiDeMo. Notably, on MSRVTT with CLIP (ViT-B/16), DiscoVLA reaches  $50.5\\%$  R@1, surpassing previous methods by  $2.2\\%$ ."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Video-Text Retrieval. Advances in vision-language pretraining [7, 12, 32-34, 42, 50, 52, 55] have achieved significant success across various downstream tasks [2, 10, 11, 18, 26, 45, 47, 54, 56, 57]. Leveraging powerful CLIP [42], recent video-text retrieval (VTR) methods [9, 14, 24, 37, 48, 49, 51] have achieved impressive performance enhancements. CLIP4Clip [37] is a pioneering CLIP-based method that aggregates image features via mean-pooling or transformers to obtain video features, inspiring subsequent studies. Additionally, Cap4Video [51] utilizes ZeroCap [46] and GPT-2 [41] to generate video-level captions as supplementary video content during both training and inference. In contrast, our DiscoVLA addresses the image-level and video-level gap by generating image-level captions used only in training to improve video-level alignment. These full fine-tuning methods impose substantial overhead from large trainable parameters.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Parameter-Efficient Transfer Learning. Parameter-efficient methods aim to adapt pre-trained models to new tasks with minimal fine-tuning. The mainstream methods in natural language processing and image tasks include techniques such as Prompt [23, 27, 28, 61, 62], Adapter [6, 17, 20, 60], and LoRA [21, 60]. Prompt [27] modifies the input space by adding learnable tokens. Adapter [20] introduces a lightweight bottleneck neural network consisting of up- and down-projection layers with a non-linear activation function. LoRA [21] aims to update up- and down-projection layers by learning low-rank decomposition matrices.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, several studies have explored parameter-efficient VTR methods [5, 22, 25, 58] to incorporate temporal modeling into the frozen image-level CLIP backbone. VoP [22] employs trainable BiLSTMs [16] to produce prompt tokens in the vision encoder. DGL [58] introduces weight-sharing layers to generate prompts for both text and video encoders. MV-Adapter [25] introduces shared bottleneck structures in both video and text branches. However, these methods overlook language and alignment discrepancies. We address these limitations with DiscoVLA, a framework that facilitates robust video-level understanding.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "19703",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/3baf7371eccbd1f136ffa4c85bcbf4d194ecc701dc4f2f62831d41c878f71323.jpg",
+        "image_caption": [
+            "Figure 2. The overall framework of DiscoVLA. Initially, we generate pseudo image captions for each sampled image. In both vision and text encoders, we utilize image-level layers to acquire pretrained image-level knowledge and employ IVFusion layers to enhance spatiotemporal information. The single video caption is encoded through the text encoder, utilizing IVFusion layer as image-level (image-lvl) layer. Finally, AlignDistill is applied to distill image-level alignment to video-level alignment. For fair comparisons with previous methods, we do not generate pseudo image captions during the inference phase."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminary",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Video-text retrieval is a task that involves retrieving relevant videos based on a given text query, or conversely, retrieving appropriate text descriptions for a video. Consistent with previous approaches [5, 22, 25, 58], we utilize the CLIP model, pre-trained on image-text data, as our backbone.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "To process a given video, we first sample a sequence of frame images uniformly, which are then input into the CLIP vision encoder to extract image features  $v^{\\mathrm{img}}$ . These features are then aggregated through temporal average pooling to get video features  $v^{\\mathrm{vid}}$ . For a given video caption, it is passed through the CLIP text encoder to extract video caption features  $t^{\\mathrm{vid}}$ . Then, we compute the cross-modal contrastive loss [40], which functions as a video-level alignment term, maximizing the video-level similarity  $\\mathrm{Sim}^{\\mathrm{vid}}$  between matched pairs:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {S i m} _ {i j} ^ {\\mathrm {v i d}} = t _ {i} ^ {\\mathrm {v i d} ^ {T}} v _ {j} ^ {\\mathrm {v i d}}, \\tag {1}\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {t 2 v} \\left(\\operatorname {S i m} ^ {\\text {v i d}}\\right) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\operatorname {S i m} _ {i i} ^ {\\text {v i d}}\\right) / \\tau)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\operatorname {S i m} _ {i j} ^ {\\text {v i d}}\\right) / \\tau)}, \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {v 2 t} \\left(\\operatorname {S i m} ^ {\\text {v i d}}\\right) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\operatorname {S i m} _ {i i} ^ {\\text {v i d}}\\right) / \\tau)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\operatorname {S i m} _ {j i} ^ {\\text {v i d}}\\right) / \\tau)}, \\tag {3}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {A} (\\operatorname {S i m} ^ {\\mathrm {v i d}}) = - \\frac {1}{2} \\left[ \\mathcal {L} _ {t 2 v} (\\operatorname {S i m} ^ {\\mathrm {v i d}}) + \\mathcal {L} _ {v 2 t} (\\operatorname {S i m} ^ {\\mathrm {v i d}}) \\right], \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            106,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $B$  is the batch size,  $\\tau$  is the temperature parameter.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. DiscoVLA",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 2, we propose DiscoVLA to address the challenges of vision, language, and alignment when transferring from image-level to video-level VL matching. First, we introduce Image-Video Features Fusion (IVFusion) in both vision and text encoders to enhance feature extraction. Next, we introduce Pseudo Image-Level Alignment (PIImgAlign) for fine-grained image-level alignment, consisting of Pseudo Image Language Generation and Image-Level Alignment. Finally, Image-to-Video Alignment Distillation (AlignDistill) is proposed to leverage image-level alignment knowledge to enhance video-level alignment.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Importantly, PImgAlign is only employed during training. For a fair comparison with previous methods and due to its generation inefficiency, PImgAlign is omitted at inference. The final similarity used for retrieval is based on video-level similarity in Eq. (1).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We focus on parameter-efficient transfer learning for video-text retrieval, where the large backbone parameters remain fixed, and only a small number of additional parameters are trained. The trainable parameters are embedded in the parameter-efficient attention of each encoder layer, as illustrated in Figure 3.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3.3. Image-Video Features Fusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Image-level and video-level variations exist in both vision and language modalities. Our proposed IVFusion fuses these image-level and video-level features in both the vision and language encoders. Below, we illustrate IVFusion's application within the vision encoder.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "header",
+        "text": "CLSTokenofVisionEncoder EOSTokenofTextEncoder --  $\\rightarrow$  UtilizedONLYduringthe training phase.",
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+    {
+        "type": "page_number",
+        "text": "19704",
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+    {
+        "type": "image",
+        "img_path": "images/0704c9a8a0461be70b62fb28713d053f6bc102bbe788c05808941ec59c7cb103.jpg",
+        "image_caption": [
+            "Figure 3. Illustration of the encoder layers for vision and text encoders. (a) Image-Level Attn operates on each of the  $F$  images or image captions individually. (b) Video-Level Attn concatenates tokens across all sampled images or image captions. (c) IVFusion Attn employs a lightweight adapter to integrate the efficiency of Image-Level Attn with the effectiveness of Video-Level Attn. Here, we illustrate the application of IVFusion within the vision encoder. The text encoder adopts the same approach for processing pseudo image captions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/46a2b4606872b486ec8096af7f0399e265e85e9f2ff67c904082ded61a9105d2.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Image-Level Attn. To achieve parameter-efficient transfer learning, we apply LoRA in the attention module of each encoder layer. As illustrated in Figure 3a,  $F \\times (N + 1)$  tokens are processed via Image-level Attn, where  $F$  denotes the number of sampled images, and  $N + 1$  represents the combination of the global CLS token and patch tokens. Image-Level Attn processes each of the  $F$  images individually, using  $N + 1$  tokens per image. However, Image-Level Attn does not encode temporal information.",
+        "bbox": [
+            88,
+            422,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Video-Level Attn. A straightforward solution is Video-Level Attn, which concatenates tokens across all sampled images, enabling the attention module to learn spatiotemporal information. As shown in Figure 3b,  $F(N + 1)$  tokens are simultaneously processed during the attention module. Due to the quadratic complexity of the attention mechanism, Image-Level Attn has a complexity of  $O(F(N)^2)$ , while Video-Level Attn has a higher complexity of  $O((FN)^2)$ .",
+        "bbox": [
+            88,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "IVFusion Attn. To combine Image-Level Attn's efficiency with Video-Level Attn's effectiveness, we introduce IV-Fusion Attn in Figure 3c. We extend Image-Level Attn by incorporating a branch that uses all CLS tokens to extract spatio-temporal information, reducing complexity to  $O(F(N)^2 + (F)^2 N)$ :",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left[ c _ {i} ^ {(1)}, \\hat {E} _ {i} \\right] = \\mathrm {A T T N} \\left(Q K V = \\left[ c _ {i} ^ {(0)}, E _ {i} ^ {(0)} \\right]\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
+            795,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left[ c _ {1: F} ^ {(2)} \\right] = \\operatorname {A T T N} \\left(Q = \\left[ c _ {1: F} ^ {(0)} \\right], K V = \\left[ c _ {1: F} ^ {(0)}, E _ {1: F} ^ {(0)} \\right]\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            112,
+            818,
+            480,
+            839
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {c} _ {i} = c _ {i} ^ {(2)} + \\sigma (c _ {i} ^ {(1)} \\mathbf {W} _ {\\mathrm {d o w n}}) \\mathbf {W} _ {\\mathrm {u p}}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            178,
+            840,
+            480,
+            862
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $c_{i}\\in \\mathbb{R}^{1\\times D}$  is CLS token of the  $i^{\\mathrm{th}}$  image and  $c_{1:F}\\in \\mathbb{R}^{F\\times D}$  are CLS tokens of all sampled images.",
+        "bbox": [
+            89,
+            869,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Similarly,  $E_{i} \\in \\mathbb{R}^{N \\times D}$  are patch tokens of the  $i^{\\text{th}}$  image and  $E_{1:F} \\in \\mathbb{R}^{FN \\times D}$  are patch tokens of all sampled images. In Eq. (7), we employ a trainable adapter to merge image-level features  $c_{i}^{(1)}$  and video-level features  $c_{i}^{(2)}$ , where  $\\mathbf{W}_{down} \\in \\mathbb{R}^{D \\times r}$  and  $\\mathbf{W}_{up} \\in \\mathbb{R}^{r \\times D}$  represent the up- and down-projection layers, and  $\\sigma$  denotes the nonlinear GELU activation [19]. Image-level features preserve pretrained spatial details, while video-level features capture temporal information. This fusion mechanism strengthens feature extraction.",
+        "bbox": [
+            511,
+            422,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our parameter-efficient vision encoder comprises both image-level and IVFusion layers. The shallow image-level layers employ Image-Level Attn to capture spatial information, while the top  $H_{v}$  IVFusion layers leverage IVFusion Attn to focus on spatio-temporal information. Consequently, our vision encoder outputs enhanced image features  $\\left\\{ v_{i}^{\\mathrm{img}} \\mid 1 \\leq i \\leq F \\right\\}$ .",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Pseudo Image-Level Alignment",
+        "text_level": 1,
+        "bbox": [
+            511,
+            710,
+            790,
+            726
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Unlike previous work focused on video-level alignment, we introduce PImgAlign to learn fine-grained image-level alignment via the decomposition of video content at the image level. To accomplish this, we first generate pseudo image captions in VTR datasets. In contrast to the straightforward sampling of images from a video, sampling image captions is impractical, as video captions generally lack the specific details needed for individual images. As a solution, we utilize the multimodal large language model (MLLM) LLaVA-NeXT [35] to generate pseudo image captions. For each sampled image from a video, we prompt the model",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19705",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "using the relevant video caption for guidance:",
+        "bbox": [
+            89,
+            90,
+            393,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The provided image is a frame sampled from the video, which describes {video caption}. Based on the video's content, provide a caption for the provided image.",
+        "bbox": [
+            120,
+            116,
+            450,
+            176
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Unlike EA-VTR [38], which uses an image captioner, our method employs a strong MLLM. By incorporating video caption guidance, it generates higher-quality image captions that align with the overall video content. Similarly to visual feature extraction, we adopt our proposed IVFusion to extract pseudo image caption features  $\\left\\{t_i^{\\mathrm{img}}|1\\leq i\\leq F\\right\\}$ .",
+        "bbox": [
+            89,
+            186,
+            482,
+            284
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given image features and pseudo image caption features from a paired video and video caption, we introduce a fine-grained image-level similarity. Since image captions are typically more concise than the images they describe, a single caption may correspond to multiple images, as shown in Figure 4d. Therefore, we calculate the maximum similarity for each image across all image captions and vice versa. Specifically, we computed a similarity matrix between image and image caption features, selecting the maximum value from each row and column to obtain the final image-level similarity:",
+        "bbox": [
+            89,
+            285,
+            483,
+            450
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {S i m} _ {i j - t 2 v} ^ {\\mathrm {i m g}} = \\frac {1}{F} \\sum_ {n = 1} ^ {F} \\max  _ {1 \\leq m \\leq F} t _ {i | n} ^ {\\mathrm {i m g} ^ {T}} v _ {j | m} ^ {\\mathrm {i m g}}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            460,
+            482,
+            503
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {S i m} _ {i j - v 2 t} ^ {\\mathrm {i m g}} = \\frac {1}{F} \\sum_ {m = 1} ^ {F} \\max  _ {1 \\leq n \\leq F} t _ {i | n} ^ {\\mathrm {i m g} ^ {T}} v _ {j | m} ^ {\\mathrm {i m g}}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            506,
+            482,
+            546
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {S i m} _ {i j} ^ {\\mathrm {i m g}} = \\frac {1}{2} \\left[ \\operatorname {S i m} _ {i j - t 2 v} ^ {\\mathrm {i m g}} + \\operatorname {S i m} _ {i j - v 2 t} ^ {\\mathrm {i m g}} \\right], \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            158,
+            549,
+            480,
+            578
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{Sim}_{ij}^{\\mathrm{img}}$  denotes the image-level similarity between the  $i^{\\mathrm{th}}$  video caption and the  $j^{\\mathrm{th}}$  video.  $t_{i|n}^{\\mathrm{img}}$  denotes the  $n^{\\mathrm{th}}$  pseudo image caption features of the  $i^{\\mathrm{th}}$  video caption and  $v_{j|m}^{\\mathrm{img}}$  denotes the  $m^{\\mathrm{th}}$  image features of the  $j^{\\mathrm{th}}$  video. PImgAlign achieves video-level alignment from the image level, effectively emphasizing spatial details.",
+        "bbox": [
+            89,
+            589,
+            482,
+            686
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "However, in the inference stage, the lack of ground truth for video captions prevents pseudo image captions generation. Additionally, MLLM introduces a computational overhead. For fair comparisons with other methods, we exclude PImgAlign during inference.",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Image-to-Video Alignment Distillation",
+        "text_level": 1,
+        "bbox": [
+            89,
+            772,
+            419,
+            787
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Pretrained CLIP demonstrates a strong capability for image-level alignment. In contrast, video-text retrieval relies on comprehensive spatio-temporal alignment. Therefore, we propose AlignDistill to distill image-level alignment knowledge into video-level alignment, thus mitigating alignment discrepancies. Then, we optimize the Kullback-Leibler divergence [30] between image-level similarity and",
+        "bbox": [
+            89,
+            794,
+            483,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "video-level similarity:",
+        "bbox": [
+            513,
+            90,
+            663,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} _ {t 2 v} ^ {\\mathrm {i m g}} = \\left[ \\mathrm {s} _ {i 1} ^ {\\mathrm {i m g}}, \\dots , \\mathrm {s} _ {i N _ {v}} ^ {\\mathrm {i m g}} \\right], \\mathcal {S} _ {v 2 t} ^ {\\mathrm {i m g}} = \\left[ \\mathrm {s} _ {1 i} ^ {\\mathrm {i m g}}, \\dots , \\mathrm {s} _ {N _ {t} i} ^ {\\mathrm {i m g}} \\right], \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            526,
+            117,
+            903,
+            137
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} _ {t 2 v} ^ {\\mathrm {v i d}} = \\left[ \\mathrm {s} _ {i 1} ^ {\\mathrm {v i d}}, \\dots , \\mathrm {s} _ {i N _ {v}} ^ {\\mathrm {v i d}} \\right], \\mathcal {S} _ {v 2 t} ^ {\\mathrm {v i d}} = \\left[ \\mathrm {s} _ {1 i} ^ {\\mathrm {v i d}}, \\dots , \\mathrm {s} _ {N _ {t i}} ^ {\\mathrm {v i d}} \\right], \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            535,
+            138,
+            903,
+            159
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {K L} = \\frac {1}{2} \\left(\\mathbf {K L} \\left(\\mathcal {S} _ {t 2 v} ^ {\\mathrm {i m g}} \\| \\mathcal {S} _ {t 2 v} ^ {\\mathrm {v i d}}\\right) + \\mathbf {K L} \\left(\\mathcal {S} _ {v 2 t} ^ {\\mathrm {i m g}} \\| \\mathcal {S} _ {v 2 t} ^ {\\mathrm {v i d}}\\right)\\right). \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            524,
+            161,
+            903,
+            189
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{s}_{ij}^{\\mathrm{img}}$  is  $\\mathrm{Sim}_{ij}^{\\mathrm{img}}$  in Eq. (10) and  $\\mathrm{s}_{ij}^{\\mathrm{vid}}$  is  $\\mathrm{Sim}_{ij}^{\\mathrm{vid}}$  in Eq. (1).  $S_{t2v}^{\\mathrm{img}}$  and  $S_{t2v}^{\\mathrm{vid}}$  denote the probability distributions for the text-to-video task, while  $S_{v2t}^{\\mathrm{img}}$  and  $S_{v2t}^{\\mathrm{vid}}$  denote those for the video-to-text task. During the inference phase, We employ enhanced video-level similarity for retrieval tasks.",
+        "bbox": [
+            511,
+            200,
+            903,
+            284
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, the overall training objective, which includes alignment loss (Eq. (4)) and distillation loss (Eq. (13)), is formulated as follows:",
+        "bbox": [
+            511,
+            285,
+            903,
+            330
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {A} (\\operatorname {S i m} ^ {\\mathrm {v i d}}) + \\alpha \\mathcal {L} _ {A} (\\operatorname {S i m} ^ {\\mathrm {i m g}}) + \\beta \\mathcal {L} _ {K L}, \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            545,
+            342,
+            903,
+            361
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha$  and  $\\beta$  are used to balance the loss.  $\\mathcal{L}_A(\\mathrm{Sim}^{\\mathrm{img}})$  is the image-level alignment loss (see Eq. (4) and (10)).",
+        "bbox": [
+            511,
+            375,
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+            407
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            511,
+            422,
+            645,
+            439
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
+        "bbox": [
+            511,
+            448,
+            720,
+            465
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following common practice, we perform evaluations on four widely used benchmarks: MSRVTT [53], LSMDC [43], ActivityNet [29], and DiDeMo [1]. We evaluate the performance using common retrieval metrics such as Recall at K (R@K and K = 1, 5, 10), the sum of these recalls (R@sum), and Mean Rank (MnR). In all experiments, the LoRA dimension and the adapter dimension  $r$  are set to 8. In Eq. 14,  $\\alpha$  and  $\\beta$  are set to 0.3 and 1.0, respectively. For the number of IVFusion layers, we set  $H_V = 4$  for the vision encoder and  $H_L = 2$  for the text encoder. Please see Appendix A for further details.",
+        "bbox": [
+            511,
+            470,
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+            637
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparisons with State-of-the-Art Methods",
+        "text_level": 1,
+        "bbox": [
+            511,
+            648,
+            888,
+            665
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We compare our proposed DiscoVLA with state-of-the-art methods on popular benchmarks such as MSRVTT, LSMDC, ActivityNet, and DiDeMo.",
+        "bbox": [
+            511,
+            672,
+            903,
+            717
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Full fine-tuning refers to CLIP4Clip-meanP [37], which averages image features along the temporal dimension. All parameter-efficient methods follow this temporal average pooling strategy to obtain the final video features. Although Prompt [27], Adapter [20], and LoRA [21] are widely adopted for parameter-efficient image and NLP tasks, they lack effective temporal modeling for video-level understanding. In contrast, methods like RAP [5], VoP [22], DGL [58], and MV-Adapter [25] focus on temporal modeling in the vision modality.",
+        "bbox": [
+            511,
+            718,
+            905,
+            869
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As shown in Table 1, on MSRVTT, our DiscoVLA with CLIP (ViT-B/32) as the backbone achieves  $47.0\\%$  R@1 in",
+        "bbox": [
+            511,
+            869,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "19706",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/811aca382ac40874239e8f66b6a50d4e99c1747b898de85248e9097c9bdde09a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\"># Params (M)</td><td colspan=\"5\">Text-to-Video</td><td colspan=\"5\">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td colspan=\"12\">CLIP (ViT-B/32)</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>43.1</td><td>70.4</td><td>80.8</td><td>194.3</td><td>16.2</td><td>43.1</td><td>70.5</td><td>81.2</td><td>194.8</td><td>12.4</td></tr><tr><td>Prompt [27]</td><td>0.08</td><td>40.4</td><td>66.3</td><td>77.3</td><td>184.0</td><td>16.7</td><td>42.2</td><td>69.7</td><td>79.2</td><td>191.1</td><td>12.4</td></tr><tr><td>Adapter [20]</td><td>0.26</td><td>41.9</td><td>69.9</td><td>78.7</td><td>190.2</td><td>14.9</td><td>43.6</td><td>69.9</td><td>80.1</td><td>193.6</td><td>11.5</td></tr><tr><td>LoRA [21]</td><td>0.49</td><td>43.7</td><td>68.9</td><td>80.4</td><td>193.0</td><td>16.0</td><td>43.0</td><td>70.2</td><td>82.2</td><td>195.4</td><td>12.0</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>44.8</td><td>71.4</td><td>81.5</td><td>197.7</td><td>14.4</td><td>44.0</td><td>71.9</td><td>82.4</td><td>198.3</td><td>10.1</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>43.5</td><td>69.3</td><td>79.3</td><td>192.1</td><td>14.8</td><td>43.6</td><td>71.2</td><td>81.2</td><td>196.0</td><td>11.0</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>44.7</td><td>70.5</td><td>79.2</td><td>194.4</td><td>16.2</td><td>42.1</td><td>70.0</td><td>80.6</td><td>192.7</td><td>13.4</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>44.6</td><td>69.9</td><td>80.3</td><td>194.8</td><td>16.3</td><td>44.5</td><td>70.7</td><td>80.6</td><td>195.8</td><td>11.5</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td><td>14.1</td><td>47.7</td><td>73.6</td><td>83.6</td><td>204.9</td><td>10.0</td></tr><tr><td colspan=\"12\">CLIP (ViT-B/16)</td></tr><tr><td>MV-Adapter [25]</td><td>3.6</td><td>46.0</td><td>72.0</td><td>82.1</td><td>200.1</td><td>-</td><td>45.6</td><td>74.0</td><td>83.8</td><td>203.4</td><td>-</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>46.5</td><td>73.9</td><td>82.0</td><td>202.4</td><td>12.1</td><td>45.3</td><td>76.4</td><td>84.8</td><td>206.5</td><td>9.1</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>47.1</td><td>72.4</td><td>81.8</td><td>201.3</td><td>12.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>47.7</td><td>72.4</td><td>82.2</td><td>202.3</td><td>12.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>48.3</td><td>71.8</td><td>80.6</td><td>200.7</td><td>13.4</td><td>45.7</td><td>74.0</td><td>82.9</td><td>202.6</td><td>10.9</td></tr><tr><td>TempMe [44]</td><td>0.50</td><td>49.0</td><td>74.4</td><td>83.3</td><td>206.7</td><td>11.9</td><td>47.6</td><td>75.3</td><td>85.4</td><td>208.3</td><td>9.0</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>50.5</td><td>75.6</td><td>83.8</td><td>209.9</td><td>12.1</td><td>49.2</td><td>76.0</td><td>84.7</td><td>209.9</td><td>8.6</td></tr></table>",
+        "bbox": [
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+            88,
+            875,
+            353
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/a5a7903817c034caa677995764389cb1cc1e597cb314aacec7b9fc5e3bfc0cca.jpg",
+        "table_caption": [
+            "Table 1. Comparisons with state-of-the-art methods on MSRVTT. # Params denotes the number of trainable parameters.  $\\uparrow$  denotes higher values represent better performance and  $\\downarrow$  denotes lower values represent better performance. The best value for each metric is highlighted in bold. R@sum is defined as the total of R@1, R@5, and R@10. The gray row represents the fully fine-tuned CLIP4Clip-meanP [37]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\"># Params (M)</td><td colspan=\"5\">Text-to-Video</td><td colspan=\"5\">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>20.7</td><td>38.9</td><td>47.2</td><td>106.8</td><td>65.3</td><td>20.6</td><td>39.4</td><td>47.5</td><td>107.5</td><td>56.7</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>20.7</td><td>40.7</td><td>49.7</td><td>111.1</td><td>59.1</td><td>21.5</td><td>40.6</td><td>50.7</td><td>112.8</td><td>50.8</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>21.1</td><td>40.9</td><td>49.6</td><td>111.6</td><td>60.1</td><td>22.3</td><td>40.3</td><td>50.7</td><td>113.3</td><td>51.1</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>21.4</td><td>39.4</td><td>48.4</td><td>109.2</td><td>64.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>23.6</td><td>42.0</td><td>52.3</td><td>117.9</td><td>52.0</td><td>22.8</td><td>41.9</td><td>51.2</td><td>115.9</td><td>46.6</td></tr></table>",
+        "bbox": [
+            122,
+            402,
+            870,
+            500
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/bd378c525d80127c71fa8ac9d0c05c1920522dc51787a2993d585255365a49ab.jpg",
+        "table_caption": [
+            "Table 2. Comparisons with state-of-the-art methods on LSMDC using CLIP (ViT-B/32)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\"># Params (M)</td><td colspan=\"5\">Text-to-Video</td><td colspan=\"5\">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>40.5</td><td>72.4</td><td>-</td><td>-</td><td>7.4</td><td>42.5</td><td>74.1</td><td>85.8</td><td>202.4</td><td>6.6</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>40.8</td><td>71.0</td><td>82.2</td><td>194.0</td><td>8.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>36.1</td><td>65.5</td><td>78.5</td><td>180.1</td><td>10.9</td><td>36.3</td><td>65.9</td><td>79.2</td><td>181.4</td><td>10.1</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>35.1</td><td>63.7</td><td>77.6</td><td>176.4</td><td>11.4</td><td>35.6</td><td>65.9</td><td>77.8</td><td>179.3</td><td>10.4</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>38.6</td><td>69.2</td><td>81.6</td><td>189.4</td><td>9.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>41.2</td><td>72.4</td><td>83.6</td><td>197.2</td><td>7.8</td><td>41.8</td><td>72.8</td><td>84.7</td><td>199.3</td><td>6.9</td></tr></table>",
+        "bbox": [
+            122,
+            518,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Comparisons with state-of-the-art methods on ActivityNet using CLIP (ViT-B/32).",
+        "bbox": [
+            225,
+            631,
+            767,
+            645
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the text-to-video task (t2v) and  $47.7\\%$  R@1 in the video-to-text task (v2t), significantly outperforming previous methods. Furthermore, when using CLIP (ViT-B/16), DiscoVLA achieves improvements of  $2.2\\%$  R@1 and  $7.5\\%$  R@sum. The comparison results on LSMDC, ActivityNet, DiDeMo are shown in Table 2-4. Our method outperforms all existing approaches across these datasets. Existing approaches overlook the critical image-to-video language and alignment discrepancies. In contrast, our proposed DiscoVLA addresses these discrepancies across all three areas: vision, language, and alignment.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            89,
+            833,
+            243,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ablation study on individual components. We evaluate the proposed components in Table 5. LoRA applies Image-Level Attn (see Figure 3a) in both the vision and text",
+        "bbox": [
+            89,
+            854,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "encoders. In B1, IVFusion significantly enhances performance by  $8.7\\%$  R@sum in t2v and  $6.7\\%$  R@sum in v2t, effectively integrating image-level and video-level features. In B2 and B3, we find that using PImgAlign or AlignDistill independently yields limited improvements. This is largely due to the notable gap between image-level and video-level (see Figure 1). Image-level PImgAlign struggles to impact video-level tasks, while AlignDistill lacks sufficient image-specific learning. When combined, however, they complement each other. PImgAlign captures fine-grained image-level alignments, and AlignDistill effectively transfers this knowledge to the video-level alignment. This improves  $1.1\\%$  R@sum in t2v and  $2.8\\%$  R@sum in v2t over B1. Finally, our full DiscoVLA improves  $9.8\\%$  R@sum in t2v and  $9.5\\%$  R@sum in v2t over LoRA.",
+        "bbox": [
+            511,
+            659,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "19707",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/a95bab51d49738d0843e405888fe37e2f953209995ba6bc1fa3e9b927bce5000.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\"># Params (M)</td><td colspan=\"5\">Text-to-Video</td><td colspan=\"5\">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>43.4</td><td>70.2</td><td>80.6</td><td>194.2</td><td>17.5</td><td>42.5</td><td>70.6</td><td>80.2</td><td>193.3</td><td>11.6</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>42.6</td><td>70.4</td><td>79.6</td><td>192.6</td><td>18.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>45.3</td><td>72.3</td><td>80.4</td><td>198.0</td><td>13.8</td><td>44.7</td><td>71.2</td><td>81.1</td><td>197.0</td><td>9.9</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>46.4</td><td>71.9</td><td>81.5</td><td>199.8</td><td>13.6</td><td>44.4</td><td>71.8</td><td>81.8</td><td>198.0</td><td>9.5</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>48.4</td><td>74.5</td><td>82.7</td><td>205.6</td><td>14.0</td><td>47.7</td><td>74.4</td><td>83.8</td><td>205.9</td><td>9.3</td></tr></table>",
+        "bbox": [
+            122,
+            88,
+            870,
+            186
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/4de793244a6ffc5548b625922d297337421431621587b97d1fbed686874bcc6f.jpg",
+        "table_caption": [
+            "Table 4. Comparisons with state-of-the-art methods on DiDeMo using CLIP (ViT-B/32)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"3\">Components</td><td rowspan=\"2\"># Params (M)</td><td colspan=\"4\">Text-to-Video</td><td colspan=\"4\">Video-to-Text</td></tr><tr><td>IVFusion</td><td>PIImgAlign</td><td>AlignDistill</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>Pretraind CLIP</td><td>X</td><td>X</td><td>X</td><td>0</td><td>30.8</td><td>53.8</td><td>63.3</td><td>147.9</td><td>26.6</td><td>50.1</td><td>62.0</td><td>138.7</td></tr><tr><td>LoRA</td><td>X</td><td>X</td><td>X</td><td>0.49</td><td>43.7</td><td>68.9</td><td>80.4</td><td>193.0</td><td>43.0</td><td>70.2</td><td>82.2</td><td>195.4</td></tr><tr><td>B1</td><td>✓</td><td>X</td><td>X</td><td>0.54</td><td>46.5</td><td>73.2</td><td>82.0</td><td>201.7</td><td>46.6</td><td>72.6</td><td>82.9</td><td>202.1</td></tr><tr><td>B2</td><td>✓</td><td>✓</td><td>X</td><td>0.56</td><td>47.0</td><td>73.1</td><td>81.3</td><td>201.4</td><td>45.7</td><td>72.9</td><td>82.4</td><td>201.0</td></tr><tr><td>B3</td><td>✓</td><td>X</td><td>✓</td><td>0.54</td><td>46.6</td><td>71.6</td><td>81.0</td><td>199.2</td><td>45.9</td><td>71.9</td><td>82.2</td><td>200.0</td></tr><tr><td>DiscoVLA</td><td>✓</td><td>✓</td><td>✓</td><td>0.56</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td><td>47.7</td><td>73.6</td><td>83.6</td><td>204.9</td></tr></table>",
+        "bbox": [
+            94,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7eb3e177f63cafd83480656c66b7d4ac4ec410146817651e40e015edc4dea50f.jpg",
+        "table_caption": [
+            "Table 5. Ablation study on the contribution of each proposed component on MSRVTT using CLIP (ViT-B/32). Pretrained CLIP denotes the zero-shot performance of CLIP without any additional training. Our proposed methods are built upon LoRA. B1, B2, and B3 denote various combinations of our proposed components."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Parameter-Efficient Attention</td><td colspan=\"4\">Text-to-Video</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>Image-Level Attn</td><td>43.7</td><td>68.9</td><td>80.4</td><td>193.0</td></tr><tr><td>Video-Level Attn</td><td>45.7</td><td>70.9</td><td>80.8</td><td>197.4</td></tr><tr><td>IVFusion Attn w/o Adapter</td><td>46.0</td><td>71.0</td><td>80.4</td><td>197.4</td></tr><tr><td>IVFusion Attn</td><td>46.5</td><td>73.2</td><td>82.0</td><td>201.7</td></tr></table>",
+        "bbox": [
+            94,
+            366,
+            480,
+            446
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ef4fc948a9d8c1a36962f76c8d7c80eec8c9313c0e05ca334a81f4e5047037b2.jpg",
+        "table_caption": [
+            "Table 6. Ablation study on IVFusion on MSRVTT using CLIP (ViT-B/32). We compare several implementations against our proposed IVFusion for Parameter-Efficient Attention (see Figure 3). Image-Level Attn represents the LoRA baseline."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Similarity in PImgAlign</td><td colspan=\"4\">Text-to-Video</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>None</td><td>46.6</td><td>71.6</td><td>81.0</td><td>199.2</td></tr><tr><td>Video-Level</td><td>46.3</td><td>72.3</td><td>81.2</td><td>199.8</td></tr><tr><td>Paired Image-Level</td><td>46.1</td><td>73.2</td><td>82.4</td><td>201.7</td></tr><tr><td>Fine-grained Image-Level</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td></tr></table>",
+        "bbox": [
+            94,
+            508,
+            480,
+            589
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Analysis of trainable parameters. The trainable parameters of our DiscoVLA consist of the LoRA and Adapter parts. As shown in Table 5, LoRA in both the vision and text encoders contain  $\\sim 0.49\\mathrm{M}$  parameters. In B1, an additional  $\\sim 0.05\\mathrm{M}$  parameters are introduced by the Adapter in the  $H_{V} = 4$  IVFusion layers of the vision encoder. In B2, an additional  $\\sim 0.02\\mathrm{M}$  parameters are introduced by the Adapter in the  $H_{L} = 2$  IVFusion layers of the text encoder, which are utilized for pseudo-image caption features in PImgAlign. Overall, the total number of trainable parameters of DiscoVLA is  $\\sim 0.56\\mathrm{M}$ .",
+        "bbox": [
+            89,
+            674,
+            482,
+            838
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation study on IVFusion. In Table 6, we compare different strategies for parameter-efficient attention in Figure 3. Video-Level Attn concatenates all tokens across sampled images to capture spatio-temporal information,",
+        "bbox": [
+            89,
+            839,
+            483,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/cabb0ee4fb81f45229bc4c29854fd64c6b8412b318c92742c1c3e31c7de73074.jpg",
+        "table_caption": [
+            "Table 7. Ablation study on similarity in PImgAlign on MSRVTT using CLIP (ViT-B/32). None represents DiscoVLA without image-level alignment optimization, shown as B3 in Table 5. Paired Image-Level is based on matched image-caption pairs. Fine-grained Image-Level represents the full DiscoVLA."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Image Caption Generation</td><td colspan=\"4\">Text-to-Video</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>DiscoVLA</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td></tr><tr><td>W/O VidCap</td><td>46.1 (-0.9)</td><td>73.0</td><td>82.1 (-0.7)</td><td>201.2 (-1.6)</td></tr></table>",
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+        "type": "text",
+        "text": "Table 8. Ablation study on image caption generation on MSRVTT using CLIP (ViT-B/32). W/O VidCap denotes generating pseudo image captions without video caption guidance.",
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+        "text": "achieving a notable  $4.4\\%$  R@sum improvement. To reduce the computational complexity, IVFusion applies spatiotemporal attention only to global CLS tokens and merges image-level features with video-level features. Without an adapter, averaging image- and video-level features results in a modest performance increase. In contrast, with a learnable adapter, IVFusion merges the features more effectively, achieving  $201.7\\%$  R@sum.",
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+        "type": "text",
+        "text": "Ablation study on similarity in PImgAlign. Table 7 demonstrates the effectiveness of our proposed fine-grained image-level similarity in PImgAlign. The similarity is computed between sampled images and pseudo image captions from a paired video and video caption. The Video-Level baseline averages the image features and pseudo-image caption features along the temporal dimension to compute the video-level similarity, replacing fine-grained image-level similarity. However, this modification leads to a notable decrease in performance, emphasizing the importance of image-level similarity in PImgAlign. In contrast, we introduce the Paired Image-Level baseline, which computes similarity based on matched image-caption pairs. Compared to Video-Level, Paired Image-Level yields a  $1.9\\%$  gain in R@sum. Moreover, we observe in Figure 4d that a single image caption may describe multiple images. Consequently, our fine-grained image-level similarity, as defined in Eq. 10, selects the maximum similarity from all available pairs, further enhancing video-level alignment.",
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+        "text": "19708",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/0b53ce37bcdb38f14d71a1c9fbed0ebd0a0de2a600f4af6fc821dc44e4c1a3bc.jpg",
+        "image_caption": [
+            "Figure 4. Visualization of discrepancies between video-level and image-level data. Each example consists of a paired video and video caption, with four sampled images from the video. Video captions are highlighted with orange solid lines, and pseudo image captions generated by LLaVA-NeXT [35] are indicated with green dashed lines. While video captions convey the general context of the video, image captions focus on the detailed context of each individual frame."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/7e4c331fad03523b338be4fd02a3c63a13d7db79123d524fa9d44dff7d422ba4.jpg",
+        "image_caption": [
+            "Figure 5. Comparison of image caption generation with (W/) and without (W/O) video caption guidance (VidCap) in PImgAlign."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ablation study on image caption generation in PImgAlign. Figure 5 and Table 8 show qualitative and quantitative evaluations of video caption guidance. In Figure 5, video captions serve as the global context that enriches the understanding of individual frames (marked in red). In Table 8, without this guidance, image captions focus only on salient regions while missing globally relevant details, leading to performance drops. In PImgAlign, we employ MLLM to process both frame images and video descriptions, generating image captions that align with the overall video content. These high-quality captions further enhance DiscoVLA's ability to learn robust image-level alignment.",
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+    },
+    {
+        "type": "text",
+        "text": "More Ablation Analysis. In Appendix B, we conduct additional ablation studies. Specifically, we evaluate the effects of hyperparameters  $\\alpha$ ,  $\\beta$ ,  $H_V$  and  $H_V$ . For fairness, all results in the main paper are reported without post-processing. Complementary evaluations with Q-Norm [4] and DSL [8]",
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+    },
+    {
+        "type": "text",
+        "text": "as post-processing methods are provided in the appendix.",
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+    {
+        "type": "text",
+        "text": "4.4. Qualitative Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To compare image-level and video-level data, we conduct a visualization experiment in Figure 4. In Figure 4a and 4b, image-level data alone fails to capture the complete content of the video. Figure 4c and 4d demonstrate a strong correlation between the video-level and image-level content, but differences across images lead to varying image captions. Visually, a video is composed of a sequence of images, incorporating temporal information. Textually, image captions are specific to individual images, while video captions describe the overall video content. These discrepancies hinder the effective transfer of image-level CLIP. Our approach addresses this issue by utilizing image-level alignment to enhance video-level alignment.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we identify three major discrepancies in the parameter-efficient transfer of image-level CLIP to videotext retrieval: vision, language, and alignment. To address these challenges, we propose DiscoVLA. Specifically, IV-Fusion fuses image-level and video-level features to tackle the vision and language discrepancies. For alignment discrepancies, we propose PImgAlign and AlignDistill, which learn and distill image-level alignment to enhance video-level alignment. Our DiscoVLA significantly outperforms existing methods, achieving state-of-the-art performance.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "Video Caption - Image Caption",
+        "bbox": [
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+    },
+    {
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+        "text": "19709",
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+    {
+        "type": "text",
+        "text": "Acknowledgment",
+        "text_level": 1,
+        "bbox": [
+            91,
+            90,
+            240,
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+    },
+    {
+        "type": "text",
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2025/DiscoVLA_ Discrepancy Reduction in Vision, Language, and Alignment for Parameter-Efficient Video-Text Retrieval/9d7a1765-54c3-41c7-9719-3ce7d4a7b6fa_origin.pdf

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2025/DiscoVLA_ Discrepancy Reduction in Vision, Language, and Alignment for Parameter-Efficient Video-Text Retrieval/full.md

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+# DiscoVLA: Discrepancy Reduction in Vision, Language, and Alignment for Parameter-Efficient Video-Text Retrieval
+
+Leqi Shen $^{1,2,4*}$  Guoqiang Gong $^{5\dagger}$  Tianxiang Hao $^{1,2}$  Tao He $^{6,7}$  Yifeng Zhang $^{5}$  Pengzhang Liu $^{5}$  Sicheng Zhao $^{2‡}$  Jungong Han $^{3}$  Guiguang Ding $^{1,2‡}$
+
+$^{1}$  School of Software  $^{2}$  BNrist  $^{3}$  Department of Automation, Tsinghua University  $^{4}$  Hangzhou Zhuoxi Institute of Brain and Intelligence
+
+$^{5}$  JD.com  $^{6}$  GRG Banking Equipment Co., Ltd.  $^{7}$  South China University of Technology
+
+# Abstract
+
+The parameter-efficient adaptation of the image-text pretraining model CLIP for video-text retrieval is a prominent area of research. While CLIP is focused on image-level vision-language matching, video-text retrieval demands comprehensive understanding at the video level. Three key discrepancies emerge in the transfer from image-level to video-level: vision, language, and alignment. However, existing methods mainly focus on vision while neglecting language and alignment. In this paper, we propose Discrepancy Reduction in Vision, Language, and Alignment (DiscoVLA), which simultaneously mitigates all three discrepancies. Specifically, we introduce Image-Video Features Fusion to integrate image-level and video-level features, effectively tackling both vision and language discrepancies. Additionally, we generate pseudo image captions to learn fine-grained image-level alignment. To mitigate alignment discrepancies, we propose Image-to-Video Alignment Distillation, which leverages image-level alignment knowledge to enhance video-level alignment. Extensive experiments demonstrate the superiority of our DiscoVLA. In particular, on MSRVTT with CLIP (ViT-B/16), DiscoVLA outperforms previous methods by  $2.2\%$  R@1 and  $7.5\%$  R@sum. The code is available at https://github.com/LunarShen/DsicoVLA.
+
+# 1. Introduction
+
+The rapid expansion of online video content has generated a growing demand for effective video-text retrieval, focusing on matching video content with relevant textual descriptions. Inspired by the success of image-text pretraining approaches such as CLIP [42], recent efforts [9, 14, 24, 37, 48, 49, 51] have increasingly focused on extend
+
+![](images/bfbe10255f720db020eda19693dec725fa3660b25e37918a8c85685474458566.jpg)  
+Figure 1. When parameter-efficient transferring image-level CLIP to video-text retrieval, we identify three key discrepancies: vision, alignment, and language. Unlike previous methods, our DiscoVLA aims to address all these discrepancies. More visualization examples are provided in Figure 4.
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Image-Level PETL Video-Level</td></tr><tr><td>Vision</td><td>Language</td><td>Alignment</td></tr><tr><td>Previous Methods</td><td>✓</td><td>×</td><td>×</td></tr><tr><td>Our DiscoVLA</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+ing these powerful capabilities to video-text retrieval tasks. However, fully fine-tuning these pretrained models requires updating numerous parameters for every dataset, resulting in large storage overhead [22, 58]. Therefore, we focus on parameter-efficient transfer learning methods, targeting strong performance with minimal trainable parameters.
+
+Although both image-text pretraining and video-text retrieval involve vision-language (VL) matching, they exhibit
+
+substantial discrepancies that hinder straightforward knowledge transfer. To be specific, image-text pretraining focuses on matching images with image captions, which represents image-level VL matching. In contrast, video-text retrieval focuses on matching videos with video captions, which represents video-level VL matching. The challenges of video-level VL matching, which demands understanding motion and time, create significant obstacles for transferring knowledge from image-text to video-text tasks.
+
+In this work, we explore the discrepancies between image-level and video-level VL matching across three key aspects: vision, language, and alignment. Videos introduce a temporal dimension, which is absent in images. Similarly, the distinction between image captions and video captions arises from the varying levels of granularity, such as isolated image descriptions versus continuous video narratives. Thus, video-level alignment is inherently more complex than image-level alignment, as it must account for intricate spatio-temporal relationships. In Figure 1, the three images correspond to "preparing food", "pouring", and "cutting", while the entire video demonstrates an instructional cooking process. Image-level VL matching focuses on isolated images, while video-level VL matching emphasizes the overall understanding of continuous segments.
+
+However, current methods [5, 22, 25, 58] struggle to fully address the discrepancies mentioned above. Some [5, 22, 25, 58] focus on the vision aspect, modeling temporal relationships to extract video-level features, while others [25, 58] attempt to reduce the modality gap between vision and language through shared parameter mechanisms. Despite these advances, these methods remain limited in both language and alignment discrepancies.
+
+To tackle these challenges, we introduce Discrepancy Reduction in Vision, Language, and Alignment, termed DiscoVLA, a novel parameter-efficient method for videotext retrieval. Unlike previous methods that target a single gap, our method aims to simultaneously reduce all significant discrepancies, as illustrated in the table of Figure 1.
+
+Specifically, we propose an Image-Video Features Fusion module (IVFusion), which addresses both vision and language discrepancies through a unified feature extraction approach. IVFusion effectively combines both image- and video-level features by utilizing a lightweight adapter. In addition to video-level alignment, we propose Pseudo Image-level Alignment (PIImgAlign) which generates pseudo image captions and learns fine-grained image-level alignment. Furthermore, to reduce alignment discrepancy, we propose Image-to-Video Alignment Distillation (AlignDistill), transferring image-level alignment knowledge to improve video-level alignment. All proposed modules prioritize parameter efficiency: IVFusion requires minimal trainable parameters, while PImgAlign and AlignDistill operate without increasing inference parameters.
+
+In summary, the main contributions are as follows:
+
+- We reveal, for the first time, the necessity of addressing all three image-to-video discrepancies—vision, language, and alignment—to achieve parameter-efficient VTR.  
+- We introduce IVFusion to fuse image- and video-level features for both vision and language gaps. PImgAlign is introduced for fine-grained image-level alignment. We introduce AlignDistill to minimize alignment gaps.  
+- Our DiscoVLA achieves state-of-the-art results on MSRVTT, LSMDC, ActivityNet, and DiDeMo. Notably, on MSRVTT with CLIP (ViT-B/16), DiscoVLA reaches  $50.5\%$  R@1, surpassing previous methods by  $2.2\%$ .
+
+# 2. Related Work
+
+Video-Text Retrieval. Advances in vision-language pretraining [7, 12, 32-34, 42, 50, 52, 55] have achieved significant success across various downstream tasks [2, 10, 11, 18, 26, 45, 47, 54, 56, 57]. Leveraging powerful CLIP [42], recent video-text retrieval (VTR) methods [9, 14, 24, 37, 48, 49, 51] have achieved impressive performance enhancements. CLIP4Clip [37] is a pioneering CLIP-based method that aggregates image features via mean-pooling or transformers to obtain video features, inspiring subsequent studies. Additionally, Cap4Video [51] utilizes ZeroCap [46] and GPT-2 [41] to generate video-level captions as supplementary video content during both training and inference. In contrast, our DiscoVLA addresses the image-level and video-level gap by generating image-level captions used only in training to improve video-level alignment. These full fine-tuning methods impose substantial overhead from large trainable parameters.
+
+Parameter-Efficient Transfer Learning. Parameter-efficient methods aim to adapt pre-trained models to new tasks with minimal fine-tuning. The mainstream methods in natural language processing and image tasks include techniques such as Prompt [23, 27, 28, 61, 62], Adapter [6, 17, 20, 60], and LoRA [21, 60]. Prompt [27] modifies the input space by adding learnable tokens. Adapter [20] introduces a lightweight bottleneck neural network consisting of up- and down-projection layers with a non-linear activation function. LoRA [21] aims to update up- and down-projection layers by learning low-rank decomposition matrices.
+
+Recently, several studies have explored parameter-efficient VTR methods [5, 22, 25, 58] to incorporate temporal modeling into the frozen image-level CLIP backbone. VoP [22] employs trainable BiLSTMs [16] to produce prompt tokens in the vision encoder. DGL [58] introduces weight-sharing layers to generate prompts for both text and video encoders. MV-Adapter [25] introduces shared bottleneck structures in both video and text branches. However, these methods overlook language and alignment discrepancies. We address these limitations with DiscoVLA, a framework that facilitates robust video-level understanding.
+
+![](images/3baf7371eccbd1f136ffa4c85bcbf4d194ecc701dc4f2f62831d41c878f71323.jpg)  
+Figure 2. The overall framework of DiscoVLA. Initially, we generate pseudo image captions for each sampled image. In both vision and text encoders, we utilize image-level layers to acquire pretrained image-level knowledge and employ IVFusion layers to enhance spatiotemporal information. The single video caption is encoded through the text encoder, utilizing IVFusion layer as image-level (image-lvl) layer. Finally, AlignDistill is applied to distill image-level alignment to video-level alignment. For fair comparisons with previous methods, we do not generate pseudo image captions during the inference phase.
+
+# 3. Methodology
+
+# 3.1. Preliminary
+
+Video-text retrieval is a task that involves retrieving relevant videos based on a given text query, or conversely, retrieving appropriate text descriptions for a video. Consistent with previous approaches [5, 22, 25, 58], we utilize the CLIP model, pre-trained on image-text data, as our backbone.
+
+To process a given video, we first sample a sequence of frame images uniformly, which are then input into the CLIP vision encoder to extract image features  $v^{\mathrm{img}}$ . These features are then aggregated through temporal average pooling to get video features  $v^{\mathrm{vid}}$ . For a given video caption, it is passed through the CLIP text encoder to extract video caption features  $t^{\mathrm{vid}}$ . Then, we compute the cross-modal contrastive loss [40], which functions as a video-level alignment term, maximizing the video-level similarity  $\mathrm{Sim}^{\mathrm{vid}}$  between matched pairs:
+
+$$
+\operatorname {S i m} _ {i j} ^ {\mathrm {v i d}} = t _ {i} ^ {\mathrm {v i d} ^ {T}} v _ {j} ^ {\mathrm {v i d}}, \tag {1}
+$$
+
+$$
+\mathcal {L} _ {t 2 v} \left(\operatorname {S i m} ^ {\text {v i d}}\right) = \frac {1}{B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(\operatorname {S i m} _ {i i} ^ {\text {v i d}}\right) / \tau)}{\sum_ {j = 1} ^ {B} \exp \left(\operatorname {S i m} _ {i j} ^ {\text {v i d}}\right) / \tau)}, \tag {2}
+$$
+
+$$
+\mathcal {L} _ {v 2 t} \left(\operatorname {S i m} ^ {\text {v i d}}\right) = \frac {1}{B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(\operatorname {S i m} _ {i i} ^ {\text {v i d}}\right) / \tau)}{\sum_ {j = 1} ^ {B} \exp \left(\operatorname {S i m} _ {j i} ^ {\text {v i d}}\right) / \tau)}, \tag {3}
+$$
+
+$$
+\mathcal {L} _ {A} (\operatorname {S i m} ^ {\mathrm {v i d}}) = - \frac {1}{2} \left[ \mathcal {L} _ {t 2 v} (\operatorname {S i m} ^ {\mathrm {v i d}}) + \mathcal {L} _ {v 2 t} (\operatorname {S i m} ^ {\mathrm {v i d}}) \right], \tag {4}
+$$
+
+where  $B$  is the batch size,  $\tau$  is the temperature parameter.
+
+# 3.2. DiscoVLA
+
+As shown in Figure 2, we propose DiscoVLA to address the challenges of vision, language, and alignment when transferring from image-level to video-level VL matching. First, we introduce Image-Video Features Fusion (IVFusion) in both vision and text encoders to enhance feature extraction. Next, we introduce Pseudo Image-Level Alignment (PIImgAlign) for fine-grained image-level alignment, consisting of Pseudo Image Language Generation and Image-Level Alignment. Finally, Image-to-Video Alignment Distillation (AlignDistill) is proposed to leverage image-level alignment knowledge to enhance video-level alignment.
+
+Importantly, PImgAlign is only employed during training. For a fair comparison with previous methods and due to its generation inefficiency, PImgAlign is omitted at inference. The final similarity used for retrieval is based on video-level similarity in Eq. (1).
+
+We focus on parameter-efficient transfer learning for video-text retrieval, where the large backbone parameters remain fixed, and only a small number of additional parameters are trained. The trainable parameters are embedded in the parameter-efficient attention of each encoder layer, as illustrated in Figure 3.
+
+# 3.3. Image-Video Features Fusion
+
+Image-level and video-level variations exist in both vision and language modalities. Our proposed IVFusion fuses these image-level and video-level features in both the vision and language encoders. Below, we illustrate IVFusion's application within the vision encoder.
+
+![](images/0704c9a8a0461be70b62fb28713d053f6bc102bbe788c05808941ec59c7cb103.jpg)  
+Figure 3. Illustration of the encoder layers for vision and text encoders. (a) Image-Level Attn operates on each of the  $F$  images or image captions individually. (b) Video-Level Attn concatenates tokens across all sampled images or image captions. (c) IVFusion Attn employs a lightweight adapter to integrate the efficiency of Image-Level Attn with the effectiveness of Video-Level Attn. Here, we illustrate the application of IVFusion within the vision encoder. The text encoder adopts the same approach for processing pseudo image captions.
+
+![](images/46a2b4606872b486ec8096af7f0399e265e85e9f2ff67c904082ded61a9105d2.jpg)
+
+Image-Level Attn. To achieve parameter-efficient transfer learning, we apply LoRA in the attention module of each encoder layer. As illustrated in Figure 3a,  $F \times (N + 1)$  tokens are processed via Image-level Attn, where  $F$  denotes the number of sampled images, and  $N + 1$  represents the combination of the global CLS token and patch tokens. Image-Level Attn processes each of the  $F$  images individually, using  $N + 1$  tokens per image. However, Image-Level Attn does not encode temporal information.
+
+Video-Level Attn. A straightforward solution is Video-Level Attn, which concatenates tokens across all sampled images, enabling the attention module to learn spatiotemporal information. As shown in Figure 3b,  $F(N + 1)$  tokens are simultaneously processed during the attention module. Due to the quadratic complexity of the attention mechanism, Image-Level Attn has a complexity of  $O(F(N)^2)$ , while Video-Level Attn has a higher complexity of  $O((FN)^2)$ .
+
+IVFusion Attn. To combine Image-Level Attn's efficiency with Video-Level Attn's effectiveness, we introduce IV-Fusion Attn in Figure 3c. We extend Image-Level Attn by incorporating a branch that uses all CLS tokens to extract spatio-temporal information, reducing complexity to  $O(F(N)^2 + (F)^2 N)$ :
+
+$$
+\left[ c _ {i} ^ {(1)}, \hat {E} _ {i} \right] = \mathrm {A T T N} \left(Q K V = \left[ c _ {i} ^ {(0)}, E _ {i} ^ {(0)} \right]\right), \tag {5}
+$$
+
+$$
+\left[ c _ {1: F} ^ {(2)} \right] = \operatorname {A T T N} \left(Q = \left[ c _ {1: F} ^ {(0)} \right], K V = \left[ c _ {1: F} ^ {(0)}, E _ {1: F} ^ {(0)} \right]\right), \tag {6}
+$$
+
+$$
+\hat {c} _ {i} = c _ {i} ^ {(2)} + \sigma (c _ {i} ^ {(1)} \mathbf {W} _ {\mathrm {d o w n}}) \mathbf {W} _ {\mathrm {u p}}, \tag {7}
+$$
+
+where  $c_{i}\in \mathbb{R}^{1\times D}$  is CLS token of the  $i^{\mathrm{th}}$  image and  $c_{1:F}\in \mathbb{R}^{F\times D}$  are CLS tokens of all sampled images.
+
+Similarly,  $E_{i} \in \mathbb{R}^{N \times D}$  are patch tokens of the  $i^{\text{th}}$  image and  $E_{1:F} \in \mathbb{R}^{FN \times D}$  are patch tokens of all sampled images. In Eq. (7), we employ a trainable adapter to merge image-level features  $c_{i}^{(1)}$  and video-level features  $c_{i}^{(2)}$ , where  $\mathbf{W}_{down} \in \mathbb{R}^{D \times r}$  and  $\mathbf{W}_{up} \in \mathbb{R}^{r \times D}$  represent the up- and down-projection layers, and  $\sigma$  denotes the nonlinear GELU activation [19]. Image-level features preserve pretrained spatial details, while video-level features capture temporal information. This fusion mechanism strengthens feature extraction.
+
+Our parameter-efficient vision encoder comprises both image-level and IVFusion layers. The shallow image-level layers employ Image-Level Attn to capture spatial information, while the top  $H_{v}$  IVFusion layers leverage IVFusion Attn to focus on spatio-temporal information. Consequently, our vision encoder outputs enhanced image features  $\left\{ v_{i}^{\mathrm{img}} \mid 1 \leq i \leq F \right\}$ .
+
+# 3.4. Pseudo Image-Level Alignment
+
+Unlike previous work focused on video-level alignment, we introduce PImgAlign to learn fine-grained image-level alignment via the decomposition of video content at the image level. To accomplish this, we first generate pseudo image captions in VTR datasets. In contrast to the straightforward sampling of images from a video, sampling image captions is impractical, as video captions generally lack the specific details needed for individual images. As a solution, we utilize the multimodal large language model (MLLM) LLaVA-NeXT [35] to generate pseudo image captions. For each sampled image from a video, we prompt the model
+
+using the relevant video caption for guidance:
+
+The provided image is a frame sampled from the video, which describes {video caption}. Based on the video's content, provide a caption for the provided image.
+
+Unlike EA-VTR [38], which uses an image captioner, our method employs a strong MLLM. By incorporating video caption guidance, it generates higher-quality image captions that align with the overall video content. Similarly to visual feature extraction, we adopt our proposed IVFusion to extract pseudo image caption features  $\left\{t_i^{\mathrm{img}}|1\leq i\leq F\right\}$ .
+
+Given image features and pseudo image caption features from a paired video and video caption, we introduce a fine-grained image-level similarity. Since image captions are typically more concise than the images they describe, a single caption may correspond to multiple images, as shown in Figure 4d. Therefore, we calculate the maximum similarity for each image across all image captions and vice versa. Specifically, we computed a similarity matrix between image and image caption features, selecting the maximum value from each row and column to obtain the final image-level similarity:
+
+$$
+\operatorname {S i m} _ {i j - t 2 v} ^ {\mathrm {i m g}} = \frac {1}{F} \sum_ {n = 1} ^ {F} \max  _ {1 \leq m \leq F} t _ {i | n} ^ {\mathrm {i m g} ^ {T}} v _ {j | m} ^ {\mathrm {i m g}}, \tag {8}
+$$
+
+$$
+\operatorname {S i m} _ {i j - v 2 t} ^ {\mathrm {i m g}} = \frac {1}{F} \sum_ {m = 1} ^ {F} \max  _ {1 \leq n \leq F} t _ {i | n} ^ {\mathrm {i m g} ^ {T}} v _ {j | m} ^ {\mathrm {i m g}}, \tag {9}
+$$
+
+$$
+\operatorname {S i m} _ {i j} ^ {\mathrm {i m g}} = \frac {1}{2} \left[ \operatorname {S i m} _ {i j - t 2 v} ^ {\mathrm {i m g}} + \operatorname {S i m} _ {i j - v 2 t} ^ {\mathrm {i m g}} \right], \tag {10}
+$$
+
+where  $\mathrm{Sim}_{ij}^{\mathrm{img}}$  denotes the image-level similarity between the  $i^{\mathrm{th}}$  video caption and the  $j^{\mathrm{th}}$  video.  $t_{i|n}^{\mathrm{img}}$  denotes the  $n^{\mathrm{th}}$  pseudo image caption features of the  $i^{\mathrm{th}}$  video caption and  $v_{j|m}^{\mathrm{img}}$  denotes the  $m^{\mathrm{th}}$  image features of the  $j^{\mathrm{th}}$  video. PImgAlign achieves video-level alignment from the image level, effectively emphasizing spatial details.
+
+However, in the inference stage, the lack of ground truth for video captions prevents pseudo image captions generation. Additionally, MLLM introduces a computational overhead. For fair comparisons with other methods, we exclude PImgAlign during inference.
+
+# 3.5. Image-to-Video Alignment Distillation
+
+Pretrained CLIP demonstrates a strong capability for image-level alignment. In contrast, video-text retrieval relies on comprehensive spatio-temporal alignment. Therefore, we propose AlignDistill to distill image-level alignment knowledge into video-level alignment, thus mitigating alignment discrepancies. Then, we optimize the Kullback-Leibler divergence [30] between image-level similarity and
+
+video-level similarity:
+
+$$
+\mathcal {S} _ {t 2 v} ^ {\mathrm {i m g}} = \left[ \mathrm {s} _ {i 1} ^ {\mathrm {i m g}}, \dots , \mathrm {s} _ {i N _ {v}} ^ {\mathrm {i m g}} \right], \mathcal {S} _ {v 2 t} ^ {\mathrm {i m g}} = \left[ \mathrm {s} _ {1 i} ^ {\mathrm {i m g}}, \dots , \mathrm {s} _ {N _ {t} i} ^ {\mathrm {i m g}} \right], \tag {11}
+$$
+
+$$
+\mathcal {S} _ {t 2 v} ^ {\mathrm {v i d}} = \left[ \mathrm {s} _ {i 1} ^ {\mathrm {v i d}}, \dots , \mathrm {s} _ {i N _ {v}} ^ {\mathrm {v i d}} \right], \mathcal {S} _ {v 2 t} ^ {\mathrm {v i d}} = \left[ \mathrm {s} _ {1 i} ^ {\mathrm {v i d}}, \dots , \mathrm {s} _ {N _ {t i}} ^ {\mathrm {v i d}} \right], \tag {12}
+$$
+
+$$
+\mathcal {L} _ {K L} = \frac {1}{2} \left(\mathbf {K L} \left(\mathcal {S} _ {t 2 v} ^ {\mathrm {i m g}} \| \mathcal {S} _ {t 2 v} ^ {\mathrm {v i d}}\right) + \mathbf {K L} \left(\mathcal {S} _ {v 2 t} ^ {\mathrm {i m g}} \| \mathcal {S} _ {v 2 t} ^ {\mathrm {v i d}}\right)\right). \tag {13}
+$$
+
+where  $\mathrm{s}_{ij}^{\mathrm{img}}$  is  $\mathrm{Sim}_{ij}^{\mathrm{img}}$  in Eq. (10) and  $\mathrm{s}_{ij}^{\mathrm{vid}}$  is  $\mathrm{Sim}_{ij}^{\mathrm{vid}}$  in Eq. (1).  $S_{t2v}^{\mathrm{img}}$  and  $S_{t2v}^{\mathrm{vid}}$  denote the probability distributions for the text-to-video task, while  $S_{v2t}^{\mathrm{img}}$  and  $S_{v2t}^{\mathrm{vid}}$  denote those for the video-to-text task. During the inference phase, We employ enhanced video-level similarity for retrieval tasks.
+
+Finally, the overall training objective, which includes alignment loss (Eq. (4)) and distillation loss (Eq. (13)), is formulated as follows:
+
+$$
+\mathcal {L} = \mathcal {L} _ {A} (\operatorname {S i m} ^ {\mathrm {v i d}}) + \alpha \mathcal {L} _ {A} (\operatorname {S i m} ^ {\mathrm {i m g}}) + \beta \mathcal {L} _ {K L}, \tag {14}
+$$
+
+where  $\alpha$  and  $\beta$  are used to balance the loss.  $\mathcal{L}_A(\mathrm{Sim}^{\mathrm{img}})$  is the image-level alignment loss (see Eq. (4) and (10)).
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Following common practice, we perform evaluations on four widely used benchmarks: MSRVTT [53], LSMDC [43], ActivityNet [29], and DiDeMo [1]. We evaluate the performance using common retrieval metrics such as Recall at K (R@K and K = 1, 5, 10), the sum of these recalls (R@sum), and Mean Rank (MnR). In all experiments, the LoRA dimension and the adapter dimension  $r$  are set to 8. In Eq. 14,  $\alpha$  and  $\beta$  are set to 0.3 and 1.0, respectively. For the number of IVFusion layers, we set  $H_V = 4$  for the vision encoder and  $H_L = 2$  for the text encoder. Please see Appendix A for further details.
+
+# 4.2. Comparisons with State-of-the-Art Methods
+
+We compare our proposed DiscoVLA with state-of-the-art methods on popular benchmarks such as MSRVTT, LSMDC, ActivityNet, and DiDeMo.
+
+Full fine-tuning refers to CLIP4Clip-meanP [37], which averages image features along the temporal dimension. All parameter-efficient methods follow this temporal average pooling strategy to obtain the final video features. Although Prompt [27], Adapter [20], and LoRA [21] are widely adopted for parameter-efficient image and NLP tasks, they lack effective temporal modeling for video-level understanding. In contrast, methods like RAP [5], VoP [22], DGL [58], and MV-Adapter [25] focus on temporal modeling in the vision modality.
+
+As shown in Table 1, on MSRVTT, our DiscoVLA with CLIP (ViT-B/32) as the backbone achieves  $47.0\%$  R@1 in
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2"># Params (M)</td><td colspan="5">Text-to-Video</td><td colspan="5">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td colspan="12">CLIP (ViT-B/32)</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>43.1</td><td>70.4</td><td>80.8</td><td>194.3</td><td>16.2</td><td>43.1</td><td>70.5</td><td>81.2</td><td>194.8</td><td>12.4</td></tr><tr><td>Prompt [27]</td><td>0.08</td><td>40.4</td><td>66.3</td><td>77.3</td><td>184.0</td><td>16.7</td><td>42.2</td><td>69.7</td><td>79.2</td><td>191.1</td><td>12.4</td></tr><tr><td>Adapter [20]</td><td>0.26</td><td>41.9</td><td>69.9</td><td>78.7</td><td>190.2</td><td>14.9</td><td>43.6</td><td>69.9</td><td>80.1</td><td>193.6</td><td>11.5</td></tr><tr><td>LoRA [21]</td><td>0.49</td><td>43.7</td><td>68.9</td><td>80.4</td><td>193.0</td><td>16.0</td><td>43.0</td><td>70.2</td><td>82.2</td><td>195.4</td><td>12.0</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>44.8</td><td>71.4</td><td>81.5</td><td>197.7</td><td>14.4</td><td>44.0</td><td>71.9</td><td>82.4</td><td>198.3</td><td>10.1</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>43.5</td><td>69.3</td><td>79.3</td><td>192.1</td><td>14.8</td><td>43.6</td><td>71.2</td><td>81.2</td><td>196.0</td><td>11.0</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>44.7</td><td>70.5</td><td>79.2</td><td>194.4</td><td>16.2</td><td>42.1</td><td>70.0</td><td>80.6</td><td>192.7</td><td>13.4</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>44.6</td><td>69.9</td><td>80.3</td><td>194.8</td><td>16.3</td><td>44.5</td><td>70.7</td><td>80.6</td><td>195.8</td><td>11.5</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td><td>14.1</td><td>47.7</td><td>73.6</td><td>83.6</td><td>204.9</td><td>10.0</td></tr><tr><td colspan="12">CLIP (ViT-B/16)</td></tr><tr><td>MV-Adapter [25]</td><td>3.6</td><td>46.0</td><td>72.0</td><td>82.1</td><td>200.1</td><td>-</td><td>45.6</td><td>74.0</td><td>83.8</td><td>203.4</td><td>-</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>46.5</td><td>73.9</td><td>82.0</td><td>202.4</td><td>12.1</td><td>45.3</td><td>76.4</td><td>84.8</td><td>206.5</td><td>9.1</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>47.1</td><td>72.4</td><td>81.8</td><td>201.3</td><td>12.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>47.7</td><td>72.4</td><td>82.2</td><td>202.3</td><td>12.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>48.3</td><td>71.8</td><td>80.6</td><td>200.7</td><td>13.4</td><td>45.7</td><td>74.0</td><td>82.9</td><td>202.6</td><td>10.9</td></tr><tr><td>TempMe [44]</td><td>0.50</td><td>49.0</td><td>74.4</td><td>83.3</td><td>206.7</td><td>11.9</td><td>47.6</td><td>75.3</td><td>85.4</td><td>208.3</td><td>9.0</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>50.5</td><td>75.6</td><td>83.8</td><td>209.9</td><td>12.1</td><td>49.2</td><td>76.0</td><td>84.7</td><td>209.9</td><td>8.6</td></tr></table>
+
+Table 1. Comparisons with state-of-the-art methods on MSRVTT. # Params denotes the number of trainable parameters.  $\uparrow$  denotes higher values represent better performance and  $\downarrow$  denotes lower values represent better performance. The best value for each metric is highlighted in bold. R@sum is defined as the total of R@1, R@5, and R@10. The gray row represents the fully fine-tuned CLIP4Clip-meanP [37].  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2"># Params (M)</td><td colspan="5">Text-to-Video</td><td colspan="5">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>20.7</td><td>38.9</td><td>47.2</td><td>106.8</td><td>65.3</td><td>20.6</td><td>39.4</td><td>47.5</td><td>107.5</td><td>56.7</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>20.7</td><td>40.7</td><td>49.7</td><td>111.1</td><td>59.1</td><td>21.5</td><td>40.6</td><td>50.7</td><td>112.8</td><td>50.8</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>21.1</td><td>40.9</td><td>49.6</td><td>111.6</td><td>60.1</td><td>22.3</td><td>40.3</td><td>50.7</td><td>113.3</td><td>51.1</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>21.4</td><td>39.4</td><td>48.4</td><td>109.2</td><td>64.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>23.6</td><td>42.0</td><td>52.3</td><td>117.9</td><td>52.0</td><td>22.8</td><td>41.9</td><td>51.2</td><td>115.9</td><td>46.6</td></tr></table>
+
+Table 2. Comparisons with state-of-the-art methods on LSMDC using CLIP (ViT-B/32).  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2"># Params (M)</td><td colspan="5">Text-to-Video</td><td colspan="5">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>40.5</td><td>72.4</td><td>-</td><td>-</td><td>7.4</td><td>42.5</td><td>74.1</td><td>85.8</td><td>202.4</td><td>6.6</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>40.8</td><td>71.0</td><td>82.2</td><td>194.0</td><td>8.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>36.1</td><td>65.5</td><td>78.5</td><td>180.1</td><td>10.9</td><td>36.3</td><td>65.9</td><td>79.2</td><td>181.4</td><td>10.1</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>35.1</td><td>63.7</td><td>77.6</td><td>176.4</td><td>11.4</td><td>35.6</td><td>65.9</td><td>77.8</td><td>179.3</td><td>10.4</td></tr><tr><td>DGL [58]</td><td>0.83</td><td>38.6</td><td>69.2</td><td>81.6</td><td>189.4</td><td>9.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>41.2</td><td>72.4</td><td>83.6</td><td>197.2</td><td>7.8</td><td>41.8</td><td>72.8</td><td>84.7</td><td>199.3</td><td>6.9</td></tr></table>
+
+Table 3. Comparisons with state-of-the-art methods on ActivityNet using CLIP (ViT-B/32).
+
+the text-to-video task (t2v) and  $47.7\%$  R@1 in the video-to-text task (v2t), significantly outperforming previous methods. Furthermore, when using CLIP (ViT-B/16), DiscoVLA achieves improvements of  $2.2\%$  R@1 and  $7.5\%$  R@sum. The comparison results on LSMDC, ActivityNet, DiDeMo are shown in Table 2-4. Our method outperforms all existing approaches across these datasets. Existing approaches overlook the critical image-to-video language and alignment discrepancies. In contrast, our proposed DiscoVLA addresses these discrepancies across all three areas: vision, language, and alignment.
+
+# 4.3. Ablation Study
+
+Ablation study on individual components. We evaluate the proposed components in Table 5. LoRA applies Image-Level Attn (see Figure 3a) in both the vision and text
+
+encoders. In B1, IVFusion significantly enhances performance by  $8.7\%$  R@sum in t2v and  $6.7\%$  R@sum in v2t, effectively integrating image-level and video-level features. In B2 and B3, we find that using PImgAlign or AlignDistill independently yields limited improvements. This is largely due to the notable gap between image-level and video-level (see Figure 1). Image-level PImgAlign struggles to impact video-level tasks, while AlignDistill lacks sufficient image-specific learning. When combined, however, they complement each other. PImgAlign captures fine-grained image-level alignments, and AlignDistill effectively transfers this knowledge to the video-level alignment. This improves  $1.1\%$  R@sum in t2v and  $2.8\%$  R@sum in v2t over B1. Finally, our full DiscoVLA improves  $9.8\%$  R@sum in t2v and  $9.5\%$  R@sum in v2t over LoRA.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2"># Params (M)</td><td colspan="5">Text-to-Video</td><td colspan="5">Video-to-Text</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>MnR↓</td></tr><tr><td>Full fine-tuning</td><td>123.54</td><td>43.4</td><td>70.2</td><td>80.6</td><td>194.2</td><td>17.5</td><td>42.5</td><td>70.6</td><td>80.2</td><td>193.3</td><td>11.6</td></tr><tr><td>RAP [5]</td><td>1.06</td><td>42.6</td><td>70.4</td><td>79.6</td><td>192.6</td><td>18.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VoPF+P [22]</td><td>0.4</td><td>45.3</td><td>72.3</td><td>80.4</td><td>198.0</td><td>13.8</td><td>44.7</td><td>71.2</td><td>81.1</td><td>197.0</td><td>9.9</td></tr><tr><td>VoPF+C [22]</td><td>14.10</td><td>46.4</td><td>71.9</td><td>81.5</td><td>199.8</td><td>13.6</td><td>44.4</td><td>71.8</td><td>81.8</td><td>198.0</td><td>9.5</td></tr><tr><td>DiscoVLA</td><td>0.56</td><td>48.4</td><td>74.5</td><td>82.7</td><td>205.6</td><td>14.0</td><td>47.7</td><td>74.4</td><td>83.8</td><td>205.9</td><td>9.3</td></tr></table>
+
+Table 4. Comparisons with state-of-the-art methods on DiDeMo using CLIP (ViT-B/32).  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">Components</td><td rowspan="2"># Params (M)</td><td colspan="4">Text-to-Video</td><td colspan="4">Video-to-Text</td></tr><tr><td>IVFusion</td><td>PIImgAlign</td><td>AlignDistill</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>Pretraind CLIP</td><td>X</td><td>X</td><td>X</td><td>0</td><td>30.8</td><td>53.8</td><td>63.3</td><td>147.9</td><td>26.6</td><td>50.1</td><td>62.0</td><td>138.7</td></tr><tr><td>LoRA</td><td>X</td><td>X</td><td>X</td><td>0.49</td><td>43.7</td><td>68.9</td><td>80.4</td><td>193.0</td><td>43.0</td><td>70.2</td><td>82.2</td><td>195.4</td></tr><tr><td>B1</td><td>✓</td><td>X</td><td>X</td><td>0.54</td><td>46.5</td><td>73.2</td><td>82.0</td><td>201.7</td><td>46.6</td><td>72.6</td><td>82.9</td><td>202.1</td></tr><tr><td>B2</td><td>✓</td><td>✓</td><td>X</td><td>0.56</td><td>47.0</td><td>73.1</td><td>81.3</td><td>201.4</td><td>45.7</td><td>72.9</td><td>82.4</td><td>201.0</td></tr><tr><td>B3</td><td>✓</td><td>X</td><td>✓</td><td>0.54</td><td>46.6</td><td>71.6</td><td>81.0</td><td>199.2</td><td>45.9</td><td>71.9</td><td>82.2</td><td>200.0</td></tr><tr><td>DiscoVLA</td><td>✓</td><td>✓</td><td>✓</td><td>0.56</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td><td>47.7</td><td>73.6</td><td>83.6</td><td>204.9</td></tr></table>
+
+Table 5. Ablation study on the contribution of each proposed component on MSRVTT using CLIP (ViT-B/32). Pretrained CLIP denotes the zero-shot performance of CLIP without any additional training. Our proposed methods are built upon LoRA. B1, B2, and B3 denote various combinations of our proposed components.  
+
+<table><tr><td rowspan="2">Parameter-Efficient Attention</td><td colspan="4">Text-to-Video</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>Image-Level Attn</td><td>43.7</td><td>68.9</td><td>80.4</td><td>193.0</td></tr><tr><td>Video-Level Attn</td><td>45.7</td><td>70.9</td><td>80.8</td><td>197.4</td></tr><tr><td>IVFusion Attn w/o Adapter</td><td>46.0</td><td>71.0</td><td>80.4</td><td>197.4</td></tr><tr><td>IVFusion Attn</td><td>46.5</td><td>73.2</td><td>82.0</td><td>201.7</td></tr></table>
+
+Table 6. Ablation study on IVFusion on MSRVTT using CLIP (ViT-B/32). We compare several implementations against our proposed IVFusion for Parameter-Efficient Attention (see Figure 3). Image-Level Attn represents the LoRA baseline.  
+
+<table><tr><td rowspan="2">Similarity in PImgAlign</td><td colspan="4">Text-to-Video</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>None</td><td>46.6</td><td>71.6</td><td>81.0</td><td>199.2</td></tr><tr><td>Video-Level</td><td>46.3</td><td>72.3</td><td>81.2</td><td>199.8</td></tr><tr><td>Paired Image-Level</td><td>46.1</td><td>73.2</td><td>82.4</td><td>201.7</td></tr><tr><td>Fine-grained Image-Level</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td></tr></table>
+
+Analysis of trainable parameters. The trainable parameters of our DiscoVLA consist of the LoRA and Adapter parts. As shown in Table 5, LoRA in both the vision and text encoders contain  $\sim 0.49\mathrm{M}$  parameters. In B1, an additional  $\sim 0.05\mathrm{M}$  parameters are introduced by the Adapter in the  $H_{V} = 4$  IVFusion layers of the vision encoder. In B2, an additional  $\sim 0.02\mathrm{M}$  parameters are introduced by the Adapter in the  $H_{L} = 2$  IVFusion layers of the text encoder, which are utilized for pseudo-image caption features in PImgAlign. Overall, the total number of trainable parameters of DiscoVLA is  $\sim 0.56\mathrm{M}$ .
+
+Ablation study on IVFusion. In Table 6, we compare different strategies for parameter-efficient attention in Figure 3. Video-Level Attn concatenates all tokens across sampled images to capture spatio-temporal information,
+
+Table 7. Ablation study on similarity in PImgAlign on MSRVTT using CLIP (ViT-B/32). None represents DiscoVLA without image-level alignment optimization, shown as B3 in Table 5. Paired Image-Level is based on matched image-caption pairs. Fine-grained Image-Level represents the full DiscoVLA.  
+
+<table><tr><td rowspan="2">Image Caption Generation</td><td colspan="4">Text-to-Video</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@sum↑</td></tr><tr><td>DiscoVLA</td><td>47.0</td><td>73.0</td><td>82.8</td><td>202.8</td></tr><tr><td>W/O VidCap</td><td>46.1 (-0.9)</td><td>73.0</td><td>82.1 (-0.7)</td><td>201.2 (-1.6)</td></tr></table>
+
+Table 8. Ablation study on image caption generation on MSRVTT using CLIP (ViT-B/32). W/O VidCap denotes generating pseudo image captions without video caption guidance.
+
+achieving a notable  $4.4\%$  R@sum improvement. To reduce the computational complexity, IVFusion applies spatiotemporal attention only to global CLS tokens and merges image-level features with video-level features. Without an adapter, averaging image- and video-level features results in a modest performance increase. In contrast, with a learnable adapter, IVFusion merges the features more effectively, achieving  $201.7\%$  R@sum.
+
+Ablation study on similarity in PImgAlign. Table 7 demonstrates the effectiveness of our proposed fine-grained image-level similarity in PImgAlign. The similarity is computed between sampled images and pseudo image captions from a paired video and video caption. The Video-Level baseline averages the image features and pseudo-image caption features along the temporal dimension to compute the video-level similarity, replacing fine-grained image-level similarity. However, this modification leads to a notable decrease in performance, emphasizing the importance of image-level similarity in PImgAlign. In contrast, we introduce the Paired Image-Level baseline, which computes similarity based on matched image-caption pairs. Compared to Video-Level, Paired Image-Level yields a  $1.9\%$  gain in R@sum. Moreover, we observe in Figure 4d that a single image caption may describe multiple images. Consequently, our fine-grained image-level similarity, as defined in Eq. 10, selects the maximum similarity from all available pairs, further enhancing video-level alignment.
+
+![](images/0b53ce37bcdb38f14d71a1c9fbed0ebd0a0de2a600f4af6fc821dc44e4c1a3bc.jpg)  
+Figure 4. Visualization of discrepancies between video-level and image-level data. Each example consists of a paired video and video caption, with four sampled images from the video. Video captions are highlighted with orange solid lines, and pseudo image captions generated by LLaVA-NeXT [35] are indicated with green dashed lines. While video captions convey the general context of the video, image captions focus on the detailed context of each individual frame.
+
+![](images/7e4c331fad03523b338be4fd02a3c63a13d7db79123d524fa9d44dff7d422ba4.jpg)  
+Figure 5. Comparison of image caption generation with (W/) and without (W/O) video caption guidance (VidCap) in PImgAlign.
+
+Ablation study on image caption generation in PImgAlign. Figure 5 and Table 8 show qualitative and quantitative evaluations of video caption guidance. In Figure 5, video captions serve as the global context that enriches the understanding of individual frames (marked in red). In Table 8, without this guidance, image captions focus only on salient regions while missing globally relevant details, leading to performance drops. In PImgAlign, we employ MLLM to process both frame images and video descriptions, generating image captions that align with the overall video content. These high-quality captions further enhance DiscoVLA's ability to learn robust image-level alignment.
+
+More Ablation Analysis. In Appendix B, we conduct additional ablation studies. Specifically, we evaluate the effects of hyperparameters  $\alpha$ ,  $\beta$ ,  $H_V$  and  $H_V$ . For fairness, all results in the main paper are reported without post-processing. Complementary evaluations with Q-Norm [4] and DSL [8]
+
+as post-processing methods are provided in the appendix.
+
+# 4.4. Qualitative Analysis
+
+To compare image-level and video-level data, we conduct a visualization experiment in Figure 4. In Figure 4a and 4b, image-level data alone fails to capture the complete content of the video. Figure 4c and 4d demonstrate a strong correlation between the video-level and image-level content, but differences across images lead to varying image captions. Visually, a video is composed of a sequence of images, incorporating temporal information. Textually, image captions are specific to individual images, while video captions describe the overall video content. These discrepancies hinder the effective transfer of image-level CLIP. Our approach addresses this issue by utilizing image-level alignment to enhance video-level alignment.
+
+# 5. Conclusion
+
+In this paper, we identify three major discrepancies in the parameter-efficient transfer of image-level CLIP to videotext retrieval: vision, language, and alignment. To address these challenges, we propose DiscoVLA. Specifically, IV-Fusion fuses image-level and video-level features to tackle the vision and language discrepancies. For alignment discrepancies, we propose PImgAlign and AlignDistill, which learn and distill image-level alignment to enhance video-level alignment. Our DiscoVLA significantly outperforms existing methods, achieving state-of-the-art performance.
+
+# Acknowledgment
+
+# References
+
+[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In Proceedings of the International Conference on Computer Vision, 2017. 5, 12  
+[2] Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C Lawrence Zitnick, and Devi Parikh. Vqa: Visual question answering. In Proceedings of the International Conference on Computer Vision, 2015. 2  
+[3] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In Proceedings of the International Conference on Computer Vision, 2021. 12  
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+This work was supported by Beijing Natural Science Foundation (No. L223023), National Natural Science Foundation of China (Nos. 62441235, 62021002, 62441614), the Key R & D Program of Xinjiang, China (2022B01006), Zhejiang Provincial Natural Science Foundation of China under Grant (No. LDT23F01013F01), CCF-DiDi GAIA Collaborative Research Funds, China Postdoctoral Science Foundation (2024M750565), Guangdong S & T Program (2024B0101040008), and the Key Realm Research and Development Program of Guangzhou (No. 2024B01W0007).  
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+        "text": "Discovering Fine-Grained Visual-Concept Relations by Disentangled Optimal Transport Concept Bottleneck Models",
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+        "text": "Yan Xie $^{1*}$  Zequn Zeng $^{1*}$  Hao Zhang $^{1\\dagger}$",
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+            "$^{1}$ National Key Laboratory of Radar Signal Processing, Xidian University, Xi'an, 710071, China",
+            "$^{2}$ State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, 710071, China"
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+        "text": "{yanxie0904, zzequn99, zhanghao_xidian}@163.com, bchen@mail.xidian.edu.cn",
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+        "text": "Abstract",
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+        "text": "Concept Bottleneck Models (CBMs) try to make the decision-making process transparent by exploring an intermediate concept space between the input image and the output prediction. Existing CBMs just learn coarse-grained relations between the whole image and the concepts, less considering local image information, leading to two main drawbacks: i) they often produce spurious visual-concept relations, hence decreasing model reliability; and ii) though CBMs could explain the importance of every concept to the final prediction, it is still challenging to tell which visual region produces the prediction. To solve these problems, this paper proposes a Disentangled Optimal Transport CBM (DOT-CBM) framework to explore fine-grained visual-concept relations between local image patches and concepts. Specifically, we model the concept prediction process as a transportation problem between the patches and concepts, thereby achieving explicit fine-grained feature alignment. We also incorporate orthogonal projection losses within the modality to enhance local feature disentanglement. To further address the shortcut issues caused by statistical biases in the data, we utilize the visual saliency map and concept label statistics as transportation priors. Thus, DOT-CBM can visualize inversion heatmaps, provide more reliable concept predictions, and produce more accurate class predictions. Comprehensive experiments demonstrate that our proposed DOT-CBM achieves SOTA performance on several tasks, including image classification, local part detection and out-of-distribution generalization. Codes are available in supplementary material.",
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+        "text": "1. Introduction",
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+        "text": "Explainable artificial intelligence aims to allow human users to comprehend and trust the output created by ma",
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+        "image_caption": [
+            "(a) Brief comparison about the coarse-grained design of vanilla CBM and fine-grained design of our proposed DOT-CBM."
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+            "(b) Inversion heatmap visualization.",
+            "Figure 1. Comparison between vanilla CBM and our proposed DOT-CBM, including architecture design and inversion heatmap for concept predictions. (a) Due to the black-box mapping from images to concepts, Vanilla CBM needs Grad-CAM [37] techniques to locate concept predictions back to image space while DOT-CBM can provide an explicit inversion heatmap visualization. (b) Due to lack of fine-grained alignment, vanilla CBM produces spurious correlations in three levels of granularity (part-background, part-object and part-part level) that mislocalizes the local concept to the background, the whole object, and incorrect local region."
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+        "text": "chine learning algorithms [6, 14]. Compared with post-hoc explanation methods [37] for black-box models, designing explicit interpretability during modeling and learning processes is beneficial to obtaining more natural explanations [8].",
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+        "text": "The Concept Bottleneck Model (CBM) [17], a representative interpretable image classification model, first predicts a pre-defined set of concepts from images and then",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "*Equal contribution. †Corresponding authors",
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+    {
+        "type": "page_number",
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+    {
+        "type": "text",
+        "text": "maps these concept descriptions to the final output class. Therefore, CBM is good at interpreting the relationship between the input image and output class predictions via intermediate human-understandable concepts. However, vanilla CBM brings these good properties at the expense of classification performance [27]. For this problem, a series of CBM variants are proposed from two lines, construct a more comprehensive and discriminative concept bank [31, 45, 46], and sophisticated architecture design [29, 38, 39] for better concept representation learning.",
+        "bbox": [
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+        "text": "Although these variants narrow the performance gap between CBMs and their black-box counterparts, their modeling method between images and concepts still has two disadvantages, as shown in Fig. 1a. Firstly, they predict multiple local concepts (i.e. local attributes like \"head\") from a global image feature, which only learns a coarse-grained relationship between the full image and all concepts. Secondly, the interpretability of prevailing CBMs mainly comes from the linear concept-class relations. The mapping from the original image to all concepts is still modeled as the black-box neural networks, which still need some post-hoc analysis [26, 27] to visualize the learned visual-concept relations. As shown in Fig. 1b, these two disadvantages often bring some visual-concept spurious correlations, where many concept predictions are frequently mis-localized in the images. These spurious correlations inherently undermine the interpretability and generalizing capabilities of CBMs.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Empirically, we categorized these visual-concept spurious correlations into three levels of granularity: i) part-background spurious correlation. This refers to a misattribution of the concept predictions of local parts to the background. ii) part-object spurious correlation. The concepts of local parts are wrongly associated with the entire object without further distinctions. iii) part-part spurious correlation. In this case, the local concepts are mislocalized to incorrect image regions. We attribute these spurious correlation problems to two key factors. The first one is the lack of fine-grained alignment between the local image regions and corresponding textual concepts, i.e. the fine-grained visual-concept relations. The second one is the overfitting of the data bias such as the statistically high co-occurrence between class and background and between concept and concept, yielding confusion to learn the difference between them. Besides, it is intuitive that the explicit interpretability modeling for the concept predictions from the images is conceivably effective in addressing these visual-concept spurious correlations.",
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+    {
+        "type": "text",
+        "text": "To this end, we propose a novel Disentangled Optimal Transport Concept Bottleneck Models, namely DOT-CBM. Compared with current CBMs, our proposed DOT-CBM can provide holistic explicit interpretability on not only the concept-class relations but also the visual region",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "concept relations. Specifically, we introduce a disentangled optimal transport (DOT) framework to ensure the intramodality disentanglement and inter-modality alignment between the image patches and textual concepts. The transport assignment solution of OT framework, is an explicit correlation matrix between image patches and pre-defined concepts, facilitating bidirectional outputs including concept predictions on concept space and concept inversion mask on the image space. Furthermore, to tackle the overfitting to the data bias, we introduce two discrete prior distributions on the patch set and the concept set to penalize the incorrect shortcut alignment between patches and concepts. In summary, our contributions are as follows:",
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+        "list_items": [
+            "- We empirically investigate the visual-concept spurious correlation phenomenon and pinpoint the two key factors of these limitations, i.e. lack of fine-grained visual-concept alignment and overfitting to the data bias.",
+            "- We propose a novel disentangled optimal transport framework to model the fine-grained visual-concept alignment and address the overfitting problems. The transport design between image patches and textual concepts provides explicit relations between image and concept predictions, which can produce concept predictions on the concept spaces and concept inversion mask on the image space.",
+            "- Extensive experiments on image classification, part detection, and out-of-distribution generalization benchmarks demonstrate our proposed DOT-CBM can achieve significant improvements over current state-of-the-art CBMs on classification accuracy, interpretability and generalizing capabilities to new distributions."
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+        "text": "2. Related Work",
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+    {
+        "type": "text",
+        "text": "Concept Bottleneck Models are a family of models [17] that first predict concepts from input images, then use these concepts to predict a downstream label. This design allows CBMs to (1) provide concept-based explanations via their predicted concepts, and (2) improve their test performance when deployed with experts via concept interventions [2, 11, 40]. Similar to previous interpretable models, CBMs also face the issue of balancing task accuracy and interoperability [10, 27]. Recent works [31, 46] has leveraged extra knowledge graph [38, 46], expert rules [18] or Large Language Models (LLMs) [22, 31, 38, 45, 47] to overcome the limitations of manually defined concept sets and has utilized pre-trained Vision-Language Models (VLMs) [24, 42, 45, 49, 50] to obtain concept predictions. These advancements have elevated the performance of CBMs to levels approaching those of black-box models.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The interpretability of prevailing CBMs primarily arises from linear relationships between concepts and classes. However, the mapping from the image to the concepts is still handled by black-box neural networks, requiring post-hoc analysis for visualization of the learned visual-concept",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "30200",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/87885aaab748a7eea38412e2b1636bcedb07341b38479ca7175d9dae9818b4f6.jpg",
+        "image_caption": [
+            "Figure 2. Overview of our proposed DOT-CBM. The overall CBM framework proceeds from left to right. In the first stage, the model transforms input images into concept activation vectors. In forward pass, local embeddings from a pre-trained Vision Transformer (ViT) and a text encoder are processed through learnable adapters to generate two feature sets (Sec. 3.2). Two orthogonal projection losses are applied to both feature sets to constrain Adapter training. An Optimal Transport (OT) algorithm optimizes the Assignment Matrix, representing the explicit correlation between concepts and image patches. Concept activation values are derived by combining this matrix with a cost matrix, and the loss is supervised by concept labels for training (Sec. 3.3). To address data bias, we use the Saliency Map from the pre-trained ViT for rough foreground-background separation as the visual prior in OT. A Conditioned Co-occurrence Matrix, based on frequency statistics, serves as the prior for concepts, enhancing the model's ability to distinguish co-occurring concepts (Sec. 3.4). In the second stage, consistent with the vanilla CBM framework, concept activation values are used to predict final class labels via a linear classification network, which is trained using class labels (Sec. 3.5)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "relations. This lack of transparency often leads to visual-concept spurious correlations, where concept predictions are frequently mis-localized in the image. We propose a disentangled OT to address these limitations.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Optimal Transport aims to find the most efficient way to map one distribution onto another by minimizing a transportation cost. In the context of machine learning, OT is widely applied in a variety of domains, including unsupervised domain adaptation [36], label representation [12, 52], cross-modal semantics [3, 4, 20, 21, 23, 25], and beyond.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this work, we further extend OT to a disentangled OT framework, to enforce the fine-grained alignment between image patches and their corresponding concepts while also ensuring disentanglement within each modality.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we begin with a brief review of the CBM problem setup in Sec. 3.1 including two stages of optimization, i.e. patches to concepts  $(f_{\\mathcal{X}\\rightarrow \\mathcal{C}})$  and concepts to classes  $(f_{\\mathcal{C}\\rightarrow \\mathcal{Y}})$ . In the first stage, to address the limited interpretation of previous CBMs in the patches-to-concepts process, we introduce a disentangled optimal transport alignment framework between patches and concepts. Concretely, in Sec. 3.2, we propose two orthogonal projection losses to disentangle the patch features and concept features. In Sec. 3.3, we introduce an optimal transport (OT) based framework to model the complex relationship",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "between patches and concepts, which can predict concepts from patches and meanwhile inverse the concept to patches to provide explanations of concept prediction. In Sec. 3.4, we integrate two prior distribution modeling to address the data bias problem. In the second stage, in Sec. 3.5, we follow vanilla CBMs and predict classes from concepts. Overall, our proposed DOT-CBM achieves holistic interpretability whether on intermediate concept predictions or on final class predictions. The whole pipeline is shown in Fig. 2.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Traditional black-box visual models aim to fit the conditional distribution  $P(y|x)$  given an a dataset  $\\mathcal{D} = \\{x_i, y_i\\}_{i=1}^N$ , where  $x_i \\in \\mathcal{X}, y_i \\in \\mathcal{Y}$  are images and class labels, respectively. Though effective, they still lack transparency to understand the underlying decision-making process to drive the final predictions.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Concept Bottleneck Models (CBMs) [17] offer an interpretable solution by first predicting human-interpretable high-level concepts before making the final prediction. Formally, the dataset is extended to  $\\mathcal{D} = \\{x_i,y_i,\\pmb {a}_i\\}_{i = 1}^N$  , where  $\\pmb {a}_i = \\{a_{ij}|a_{ij}\\in \\{0,1\\} \\}_{j = 1}^M$  represents a binary concept activation label.  $a_{ij} = 1$  indicates the presence of a specific high-level concept  $c_{j}$  in image  $x_{i}$  , while  $a_{ij} = 0$  means the absence.  $c_{j}$  is concept from the pre-defined concept set  $\\mathcal{C} = \\{c_j\\}_{j = 1}^M$  . The optimization process of CBMs can be divided into two-stage [26, 35]: I) they first leverage a con",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "30201",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "cept predictor  $f_{\\mathcal{X}\\to \\mathcal{C}}:\\mathbb{R}^{H\\times W\\times C}\\to \\mathbb{R}^M$  to map the input data  $x$  to the concept activation vector  $\\pmb {a}\\in \\mathbb{R}^{M}$  . 2) Subsequently, a target predictor  $f_{\\mathcal{C}\\rightarrow \\mathcal{Y}}:\\mathbb{R}^{M}\\to \\mathbb{R}^{N_{y}}$  maps the concept activation vector  $\\pmb{a}$  to the final label  $y$  . This structure enhances the interpretability of the model, as the intermediate concept predictions provide interpretability into the model's final decision. However, the interpretability from image to concept is un-explored.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Disentanglement on Local representations",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Disentangled visual patch features  $\\widetilde{\\mathcal{P}}$ . As previously discussed, current CBMs typically associate multiple local concepts with a global image feature, which leads to coarse-grained correspondences. In this paper, we adopt the pretrained vision transformer (ViT) [1] model, which has been approved to exhibit better spatial location information extraction than CNN [34], to extract local patch features to represent the local image regions.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Specifically, as shown in the left part of Fig. 2, ViT uniformly divides the full image  $x \\in \\mathbb{R}^{H \\times W \\times C}$  into  $N$  non-overlapping patches  $\\{I_{pi} \\in \\mathbb{R}^{P_h \\times P_w}\\}_{i=1}^N$ . After linearly projecting these patches into a  $d$ -dimension embedding space and flattening all patch embeddings into a sequence, we can get an initialized patch embedding matrix  $X_P \\in \\mathbb{R}^{N \\times d}$ . To extract the global image feature, ViT concatenates a learnable special token [CLS] with  $X_P$ . Besides, in order to preserve the spatial information of images, ViT adds a learnable position embedding  $X_{pos} \\in \\mathbb{R}^{(N+1) \\times d}$  and we get the input embeddings  $X$  for ViT:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {P} = \\left[ I _ {p 1} \\cdot W _ {p}, \\dots , I _ {p N} \\cdot W _ {p} \\right], \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX = \\left[ \\left[ \\mathrm {C L S} \\right], X _ {P} \\right] + X _ {\\text {p o s}}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            183,
+            565,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{p}\\in \\mathbb{R}^{(P_{h}\\cdot P_{w}\\cdot C)\\times d}$  is the patch embedding projection weights. Then, the pre-trained ViT  $E_I$  to map the input embeddings  $X$  into the global feature  $g_{I}$ , and patch features  $\\mathcal{P} = \\{p_i\\}_{i = 1}^N$ :",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n[ g _ {I}, \\mathcal {P} ] = E _ {I} (X), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We empirically find that the patch features within the object regions are highly similar which is good for object representation, but bad for distinguishing local parts within the object region. Thus, we fit a learnable visual adapter  $A_v$  on the  $\\mathcal{P}$  and map the patch features within the foreground region to a disentangled unit hypersphere by introducing a visual orthogonal projection (VOP) regularizer as:",
+        "bbox": [
+            89,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS _ {I} = g _ {I} \\cdot P, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            243,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\langle A _ {v} (p _ {i}), A _ {v} (p _ {j}) \\rangle = \\frac {A _ {v} (p _ {i}) \\cdot A _ {v} (p _ {j})}{\\| A _ {v} (p _ {i}) \\| \\| A _ {v} (p _ {j}) \\|}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V O P}} = \\underset {\\left(p _ {i}, p _ {j}\\right) \\sim \\mathcal {P}} {\\mathbb {E}} \\left[ S _ {I} (i) \\cdot S _ {I} (j) \\cdot \\left\\langle A _ {v} \\left(p _ {i}\\right), A _ {v} \\left(p _ {j}\\right) \\right\\rangle \\right] \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            107,
+            872,
+            482,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $S_{I}$  is the saliency map to distinguish foreground and background,  $\\langle \\cdot ,\\cdot \\rangle$  is the cosine similarity. Finally, we get the disentangled patch features  $\\widetilde{\\mathcal{P}} = \\{\\widetilde{p_i} = A_v(p_i)\\}_{i = 1}^N$  Disentangled textual concept features  $\\widetilde{\\mathcal{T}}$ . For concept feature extraction, following [22, 29, 45, 47], we utilize a pre-trained text encoder  $E_{T}$  to compute concept embeddings  $\\mathcal{T} = \\{t_j = E_T(c_j)\\}_{j = 1}^M$ . Similarly, we fit a learnable textual adapter  $A_{t}$  and introduce a textual orthogonal projection (TOP) regularizer to disentangle the concept features in a unit hyper-sphere, as:",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {T O P}} = \\underset {(t _ {i}, t _ {j}) \\sim \\mathcal {T}} {\\mathbb {E}} [ \\langle A _ {t} (t _ {i}), A _ {t} (t _ {j}) \\rangle ], \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Consequently, we get the disentangled concept features  $\\widetilde{\\mathcal{T}} = \\{\\widetilde{t_j} = A_t(t_j)\\}_{j = 1}^M.$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Patch-concept alignment via optimal transport",
+        "text_level": 1,
+        "bbox": [
+            511,
+            328,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Now, we have the disentangled patch feature set  $\\widetilde{\\mathcal{P}}$  and disentangled concept feature set  $\\widetilde{\\mathcal{T}}$ , we need to model the relationship  $\\mathbf{Q}$  between these two sets and derive the concept activation vector  $\\hat{\\pmb{a}}$  based on the input image. As a complex many-to-many alignment problem, we propose an optimal transport (OT) based binary cross-entropy loss to tackle these problems. Our goal is to correctly align the patch features and concept features with the same semantics.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Assume that these two sets  $\\widetilde{\\mathcal{P}}$  and  $\\widetilde{\\mathcal{T}}$  follow two discrete probability distributions  $\\Theta \\in \\mathbb{R}^N$  and  $\\Gamma \\in \\mathbb{R}^M$  on the  $d$ -dimension embedding space, respectively:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\Theta} = \\sum_ {i = 1} ^ {N} \\theta_ {i} \\delta_ {p _ {i}}, \\quad \\boldsymbol {\\Gamma} = \\sum_ {j = 1} ^ {M} \\gamma_ {j} \\delta_ {c _ {j}}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            596,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\pmb{\\theta} \\in \\Sigma^{N}$  and  $\\pmb{\\gamma} \\in \\Sigma^{M}$ , the simplex of  $\\mathbb{R}^N$  and  $\\mathbb{R}^{M}$ , denote the probability values of the discrete states with satisfaction that  $\\sum_{i=1}^{N} \\theta_{i} = 1$  and  $\\sum_{j=1}^{M} \\gamma_{j} = 1$ .  $\\delta_{e}$  refers to a point mass located at coordinate  $e \\in \\mathbb{R}^{d}$ . The prior modeling of  $\\pmb{\\theta}$  and  $\\pmb{\\gamma}$  are shown in the Sec. 3.4.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To get the transport assignment  $\\mathbf{Q}$  between  $\\Theta$  and  $\\Gamma$ , the objective of OT is formulated as the optimization problem:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {Q} \\in \\mathcal {Q}} \\sum_ {i, j} q _ {i j} d _ {i j} - \\varepsilon H (\\mathbf {Q}) \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {s . t .} \\mathcal {Q} = \\left\\{\\mathbf {Q} \\in \\mathbb {R} _ {+} ^ {N \\times M} \\mid \\mathbf {Q} \\mathbf {1} _ {M} = \\boldsymbol {\\theta}, \\mathbf {Q} ^ {\\top} \\mathbf {1} _ {N} = \\boldsymbol {\\gamma} \\right\\}.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{Q}$  is the set of doubly stochastic matrices  $\\mathbf{Q} = [q_{ij}]_{N\\times M}$ , denotes the corresponding transport assignment where  $q_{ij}$  represents the probabilities of aligning  $p_i$  with  $t_j$ .  $\\mathbf{1}^M$  is the  $M$ -dimensional vector of ones.  $d_{ij} = d(p_i,t_j) = (1 - \\langle p_i,t_j\\rangle)\\geq 0$  is the transport cost between the two points  $p_i$  and  $s_j$  and we use the cosine distance to compute cost matrix  $\\mathbf{D}$ . The optimal  $\\mathbf{Q}^*$  of (9) has a simple normalized exponential matrix solution by Sinkhorn fixed point iterations [7],",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "footer",
+        "text": "30202",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/ea76a7dba2a4f3ab732113d26928c8cbb74c4ad73f1fd3de7a85d95713606a83.jpg",
+        "image_caption": [
+            "Figure 3. Conditioned co-occurrence matrix of concept labels."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            150,
+            88,
+            428,
+            270
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Q} ^ {*} = \\operatorname {S i n k h o r n} (\\mathbf {D}, \\boldsymbol {\\theta}, \\gamma), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            196,
+            325,
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+            340
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After obtaining the optimal transport assignment  $\\mathbf{Q}^*$ , the OT distance between the two sets is expressed as:",
+        "bbox": [
+            89,
+            349,
+            482,
+            378
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nd _ {O T} = \\sum_ {i, j} q _ {i j} d _ {i j} \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            225,
+            391,
+            482,
+            424
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For the concept embedding  $t_j$ , we only consider the minimum distance  $d_{OT_j} = \\min_i(q_{ij}d_{ij})$  between this concept embedding  $t_j$  and all patch embeddings to facilitate the concept activation value prediction  $(x\\rightarrow \\mathcal{C})$ , the predicted concept activation vector  $\\hat{\\pmb{a}}$  are stated as:",
+        "bbox": [
+            89,
+            435,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\boldsymbol {a}} = \\left\\{\\hat {a} _ {j} \\mid \\hat {a} _ {j} = \\sigma \\left(1 - d _ {O T _ {j}}\\right) \\right\\} _ {j = 1} ^ {M}. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            173,
+            521,
+            480,
+            542
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma$  is the sigmoid function. Moreover, we can inverse specific concepts to the image patches based on  $\\mathbf{Q}^*$ , and get the inversion mask  $m_j$  of concept  $c_j$ , as:",
+        "bbox": [
+            89,
+            551,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nm _ {j} = \\left[ q _ {1 j}, q _ {2 j}, \\dots , q _ {N j} \\right]. \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "By utilizing OT distance between patches and concepts as the patch-concept transport, our OT-based binary cross-entropy loss  $\\mathcal{L}_{\\mathrm{concept}}$  are as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {c o n c e p t}} = - \\mathbb {E} [ \\boldsymbol {a} \\log (\\hat {\\boldsymbol {a}}) + (1 - \\boldsymbol {a}) \\log (1 - \\hat {\\boldsymbol {a}}) ] \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            712
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Now, we can get the total objective of stage 1  $(f_{\\mathcal{X}\\to \\mathcal{C}})$ , as:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {f, x \\rightarrow c} = \\lambda_ {1} \\mathcal {L} _ {\\mathrm {V O P}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {T O P}} + \\lambda_ {3} \\mathcal {L} _ {\\text {c o n c e p t}}, \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_1, \\lambda_2, \\lambda_3$  are the hyperparameters.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The obtained assignment  $\\mathbf{Q}^{*} = [q_{i,j}]_{N\\times M}$  indicates the relationship between patches and concepts, where  $q_{i,j}$  represent correlation between patch  $p_i$  and concept  $c_{j}$ . Consequently, based on  $\\mathbf{Q}^*$ , we can obtain concept activation  $\\pmb{a}$  (Eq.(12)) based on the image features  $(x\\to \\mathcal{C})$  and meanwhile inverse the concept to the original image patches (Eq.(13))  $(\\mathcal{C}\\rightarrow x)$  to provide explicit interpretation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.4. Prior distributions Modeling",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The prior distributions of  $\\theta$  and  $\\gamma$  of OT are typically uniform distributions, which is sub-optimal for our task. Considering the part-background spurious correlation and part-part spurious correlation problem mentioned in Fig. 1b, we propose two prior distribution modeling in this section to address these limitations, respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Patch set prior  $\\theta$ . We attribute the part-background spurious correlation phenomenon to the high co-occurrence of some classes and backgrounds, such as \"seabird\" and \"water\". To solve this biased association between object concepts and the background, we use saliency map  $S_I$  from Eq. (4) to encourage the transports between the patch features within foreground regions and concepts and penalize the transports of background regions. Specifically, the prior distribution of patch set  $\\theta$  are formulated as:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\theta} = \\operatorname {S o f t m a x} \\left(S _ {I}\\right), \\tag {16}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Concept set prior  $\\gamma$ . As illustrated in Fig. 3, some concepts are highly co-occurrent. These concept label biases lead to the model's confusion between these concepts, yielding the part-part spurious correlation phenomenon. To address this problem, we employ the statistical co-occurrence matrix of the training dataset to facilitate the prior distribution modeling of  $\\gamma$ , aiming to penalize those concepts with high co-occurrence with other concepts.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Specifically, for a dataset with  $M$  concepts and  $K$  classes, class-concept label form a matrix  $L = [l_{i,j}]_{K\\times M}$  where  $l_{i,j}$  represents the activation value of the  $j$ -th concept in the concept label for the  $i$ -th class. First, we count the co-occurrence frequencies of each pair of concepts. Then, we normalize these counts by the total number of times each concept is activated, resulting in the conditional co-occurrence matrix. The conditional co-occurrence vector  $r_i$  is calculated as follows:",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr _ {i} = \\sum_ {j = 1} ^ {M} \\left(\\frac {\\sum_ {k = 1} ^ {K} L _ {k i} \\cdot L _ {k j}}{\\sum_ {k = 1} ^ {K} L _ {k i}}\\right) \\tag {17}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The concept set prior distribution  $\\gamma$  is then derived from the conditional co-occurrence vector as follows:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\gamma = 1 - \\operatorname {S o f t m a x} \\left(r _ {i}\\right) \\tag {18}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This prior modeling ensures that those concepts with high co-occurrence with other concepts will be penalized.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Concept  $\\rightarrow$  class prediction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Now, we already finished the first stage which obtains the intermediate concept activation predictions  $\\pmb{a}$ . In the second stage, our goal is to learn the association between concept and final class prediction similar to vanilla CBM. Specifically, we can map the  $\\pmb{a}$  to final output  $\\hat{y}$ , as:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {y} = W _ {F} \\cdot \\boldsymbol {a}, \\tag {19}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "30203",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The classification objective of stage 2  $(f_{\\mathcal{C}\\to \\mathcal{Y}})$  is the cross-entropy loss  $\\mathcal{L}_{\\mathrm{CE}}(y,\\hat{y})$",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiment",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the effectiveness of our proposed DOT-CBM, we conduct experiments on the image classification task and part detection task. To further demonstrate our method's abilities to reduce spurious correlations, we also conduct experiments on out-of-distribution generalization tasks. For the concept-to-class linear layer, we omit explicit sparse regularization (e.g., L1 penalties) during training. Despite this, the model spontaneously exhibits significant sparsity in the weight matrix due to two orthogonal losses. Comprehensive training details, training efficiency results, quantitative evaluations of sparsity and additional experiments are listed in the Appendix.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Metrics",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For the image classification task. We evaluate our method on the CUB [41] and AwA2 [43] datasets, which are widely adopted in the interpretable community. The CUB dataset contains 11,788 images of 200 bird subcategories, and we use the official train-test split for fine-grained image classification. The AwA2 dataset includes 37,322 images across 50 animal categories, and we follow the same train-test split as in [17]. Additionally, we conduct experiments on the larger and more complex ImageNet-1K[9] and CIFAR-100[19] datasets. On these classification datasets, we leverage the classification accuracy to measure the performance of our method. We also conducted experiments on a more complex dataset (Places365), where the complexity arises from discriminative content being image backgrounds. Quantitative and qualitative results are listed in Appendix.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For the part detection task. To evaluate the accuracy of the inversion mask produced by DOT-CBM, we evaluate our method on some part detection benchmarks, including CUB dataset, Part-ImageNet [13] and PASCAL-Part [5] datasets, which are widely used for part segmentation tasks. We also test our model on the RIVAL-10 dataset [28], which is specifically designed for evaluating model interpretability. On the CUB dataset, we obtain the bounding boxes for local parts that are commonly used in part detection tasks[44, 51]. The RIVAL-10 dataset consists of over 26K images retrieved from the ImageNet dataset according to the CIFAR-10 [19] categories, and it includes part attribute segmentation masks for the main subjects in the images. The Part-ImageNet and PASCAL-Part datasets are part segmentation datasets that provide fine-grained attribute segmentation masks. We follow [30] and preprocess these datasets by focusing on the animal data and merging overly fine-grained part attribute masks. The detailed data preprocessing procedures are described in the Appendix. We use the",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "bounding boxes of these masks as the ground truth of part detection. On these datasets, we use the  $mAP_{0.5}$  metric to evaluate the precision of predicted concept inversion masks.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We employ the pre-trained DINOV2 ViT-L/14 [32] as the image encoder and pre-trained CLIP text encoder [33] as the text encoder. The feature dimension in both encoders is  $d = 768$ . We resize all images to  $H \\times W = 252 \\times 252$  as input resolution in both training and testing phases throughout all experiments. For both adapter  $A_v$  and  $A_t$ , we use a three-layer MLP with ReLU activation functions and a dropout rate of 0.4. The optimization of DOT-CBM is done by AdamW with an initialized learning rate of  $1e - 4$ , and decreased every ten epochs by a factor of 0.5. We set weight decay of 10-5. Batch sizes are set as 128 with maximally 200 training epochs. All experiments are conducted on a single RTX 3090 GPU and our model is implemented in PyTorch. We set  $\\lambda_1 = 0.15$ ,  $\\lambda_2 = 0.2$ ,  $\\lambda_3 = 0.8$  for CUB dataset. Hyperparameters setting on other datasets and the range ablation study are in the Appendix.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Main Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare our proposed DOT-CBM with several state-of-the-art CBM baselines from the literature. Vanilla-CBM [17] is the first CBM model, proposing the design of the intermediate concept layer. Vanilla-CBM introduces three training strategies, i.e. independent, sequential and joint training, in which the independent training can achieve the best interpretation [26]. Our two-stage optimization belongs to the independent training strategy. Additionally, we compare our performance with recent CBM variants including CEM [48], LaBo [45], SparseCBM [38], CoopCBM [39]. Due to the fact that pre-defined concepts and image backbone will significantly affect the final performance. For a fair comparison, we re-implement all baselines with the high-quality concepts produced by the CDL [47] and a pre-trained ViT backbone to extract image features, the same as our method. The performance of all re-implemented baselines exceeds the best performance reported in their papers.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Image classification results. As shown in Table 1, we compare our proposed DOT-CBM with all baselines on four common image classification benchmarks. The classification results show that the DOT-CBM achieves superior performance on three benchmarks. Specifically, the performance improvements over the state-of-the-art (SOTA) are 0.91 points on ImageNet, 3.29 points on CUB, and 1.08 points on CIFAR100. Our method only lags behind CoopCBM by 0.25 points on the AwA2 dataset.",
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+    },
+    {
+        "type": "text",
+        "text": "Part detection results. A key property of our proposed DOT-CBM model is able to provide explicit explanations for the concept predictions, via the locate the concept to the",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "30204",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2fb6c11fcb69f793cac2a8e72ab4e09ac7d847b3a45326b8cc983657e3f6155e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Classification Accuracy (↑)</td><td colspan=\"4\">Part Detection mAP0.5 (↑)</td></tr><tr><td>ImageNet</td><td>CUB</td><td>CIFAR100</td><td>AWA2</td><td>PartImageNet</td><td>CUB</td><td>RIVAL</td><td>PASCAL-Parts</td></tr><tr><td>Vanilla-CBM [17]</td><td>79.17</td><td>78.32</td><td>80.04</td><td>93.15</td><td>26.94</td><td>27.02</td><td>26.76</td><td>17.32</td></tr><tr><td>CEM [48]</td><td>81.29</td><td>80.47</td><td>81.23</td><td>95.92</td><td>29.19</td><td>30.86</td><td>30.83</td><td>20.85</td></tr><tr><td>LaBo [45]</td><td>82.93</td><td>81.30</td><td>84.10</td><td>96.92</td><td>38.27</td><td>39.28</td><td>40.34</td><td>30.17</td></tr><tr><td>SparseCBM [38]</td><td>82.85</td><td>82.07</td><td>84.75</td><td>95.56</td><td>39.84</td><td>40.23</td><td>40.68</td><td>33.71</td></tr><tr><td>CoopCBM [39]</td><td>82.73</td><td>82.10</td><td>84.66</td><td>97.08</td><td>41.17</td><td>45.16</td><td>43.82</td><td>35.75</td></tr><tr><td>DOT-CBM</td><td>83.84(+0.91)</td><td>85.39(+3.29)</td><td>85.83(+1.08)</td><td>96.83(-0.25)</td><td>50.12(+8.95)</td><td>53.47(+8.31)</td><td>50.93(+7.11)</td><td>44.18(+8.43)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5448c68cfb65eff58dcded3813da7d0a5836f418d1ce6398a436420e81a34413.jpg",
+        "table_caption": [
+            "Table 1. Performance comparison of Classification Accuracy (%) and Part Detection  $\\left( {mA}{P}_{0.5}\\right)$  ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">CUB</td><td colspan=\"2\">Dogs</td></tr><tr><td>ID</td><td>OOD</td><td>ID</td><td>OOD</td></tr><tr><td>Vanilla-CBM [17]</td><td>86.9</td><td>27.7</td><td>87.3</td><td>29.4</td></tr><tr><td>CEM [48]</td><td>84.0</td><td>34.0</td><td>83.8</td><td>36.5</td></tr><tr><td>LaBo [45]</td><td>85.3</td><td>39.4</td><td>85.9</td><td>41.7</td></tr><tr><td>Sparse-CBM [38]</td><td>84.5</td><td>35.8</td><td>85.8</td><td>38.6</td></tr><tr><td>Coop-CBM [39]</td><td>85.8</td><td>36.2</td><td>86.1</td><td>40.3</td></tr><tr><td>DOT-CBM w/o. prior</td><td>86.5</td><td>36.9</td><td>87.0</td><td>40.8</td></tr><tr><td>DOT-CBM w. prior</td><td>87.2</td><td>49.7</td><td>89.1</td><td>52.4</td></tr><tr><td></td><td>(+0.3)</td><td>(+10.3)</td><td>(+1.8)</td><td>(+10.7)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Performance comparison of OOD generalization.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "original image space, i.e. the concept inversion mask derived from the transport assignment. This concept inversion mask in the image space indicates the most influential image region contributing to the concept predictions. By contrast, all previous CBMs, using a black-box neuron network to model the mapping from global image features to concept predictions, can only inverse the concept prediction to the image space via the post-hoc Grad-CAM. To evaluate the accuracy of concept inversion mask, we conduct experiments on the part detection datasets and use the groundtruth bounding boxes of the parts to assess the localization performance. To measure the similarity with groundtruths, we need to process our concept inversion mask output and heatmap outputs of baselines (derived from Grad-CAM) into rectangle boxes format. Specifically, we set the threshold at 0.6 of the maximum peak value output of the mask. The local regions above this threshold are considered as the corresponding regions of the concept in the original image. We take the bounding box that encloses this region as the predicted bounding box for the concept.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "From Table. 1, we can observe that DOT-CBM significantly surpasses all baselines (average 8 points improvements), demonstrating the superiority of our design for fine-grained patch-concept alignment. The Coop-CBM achieves performance that is second only to ours due to the introduction of an orthogonality loss similar to our proposed textual orthogonal project  $\\mathcal{L}_{\\mathrm{TOP}}$ , which further proves the validity of our proposed disentangled OT framework. Consequently,",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "DOT-CBM can inherently produce accurate and explicit explanations for intermediate concept predictions. We also conduct comparison with other ViT-appropriate attribution method. Results shown in Appendix.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Out-of-distribution generalization",
+        "text_level": 1,
+        "bbox": [
+            511,
+            347,
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+            363
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "As discussed in the previous sections, there exists data bias in many datasets, leading to shortcut learning. For example, classifying a dog as a huskie based on the snowy background due to the high co-occurrence in the training set, which is analogous to the part-background spurious correlation discussed in Fig. 1b. To validate the effectiveness of our method with background shifts, we follow [39] to segment the foreground object in CUB[41] and Dogs[15] datasets using SAM [16] with bounding box annotations and add a colored background to all images. Each class is associated with a randomly generated color background with an  $80\\%$  probability in the training set. The in-distribution (ID) test set contains images with a similar color background probability as the training set, while the color similarity of out-of-distribution (OOD) test set is reduced to  $30\\%$ . Results are shown in Table 2. As we can see, DOT-CBM can achieve comparable results on ID set and surpass the performance of baselines on the OOD set by a large margin, demonstrating that DOT-CBM can effectively decrease the biased association between object concepts and background. To investigate whether the improvements of tackling part-background spurious correlation are derived from the patch set prior modeling as mentioned in Sec. 3.4, we conduct ablations for the patch set prior and demonstrate the efficacy of patch set prior  $\\theta$ .",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+            756,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this section, we investigate the effects of each component in our framework. Ablation results are listed in Table 3. The baseline has the same trainable networks as DOT-CBM, including two adapters and a linear classification layer. The baseline replaces the OT assignment with a dot product of patch features and concept features.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effect of OT design (OT). For the comparison between the first row and second row in Table. 3, we can find the",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "page_number",
+        "text": "30205",
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+        "img_path": "images/d2bbfdaf42f92d062a40b52d41705ee27235cfbf92af7caf2552997f2c329b90.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">OT</td><td rowspan=\"2\">Prior</td><td rowspan=\"2\">LrD</td><td colspan=\"4\">Classification Accuracy (↑)</td><td colspan=\"4\">Part Detection mIOU (↑)</td></tr><tr><td>ImageNet</td><td>CUB</td><td>CIFAR100</td><td>AWA2</td><td>PartImageNet</td><td>CUB</td><td>RIVAL</td><td>PASCAL-Parts</td></tr><tr><td>X</td><td>X</td><td>X</td><td>81.60</td><td>80.92</td><td>82.73</td><td>96.07</td><td>0.35</td><td>0.41</td><td>0.37</td><td>0.28</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>82.03</td><td>81.75</td><td>82.91</td><td>96.24</td><td>0.42</td><td>0.49</td><td>0.42</td><td>0.34</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>83.22</td><td>84.92</td><td>85.49</td><td>96.47</td><td>0.50</td><td>0.61</td><td>0.53</td><td>0.46</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>82.73</td><td>82.10</td><td>84.66</td><td>97.08</td><td>0.47</td><td>0.58</td><td>0.49</td><td>0.41</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>83.84</td><td>85.39</td><td>85.83</td><td>96.83</td><td>0.52</td><td>0.66</td><td>0.54</td><td>0.49</td></tr></table>",
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+        "type": "text",
+        "text": "Table 3. Ablation studies on image classification and part detection. OT, Prior, and LrD denote the optimal transport design, prior distribution modeling, and local representation disentanglement.",
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+        "type": "image",
+        "img_path": "images/1d71a38ad4c7dbfe9cb6d33181883381d0462270320f24079438f568e80b6584.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative results for the concept inversion. VanillaCBM and CoopCBM adopt Grad-CAM to provide a concept inversion heatmap, while our proposed DOT-CBM can generate the inversion mask on its own."
+        ],
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+    {
+        "type": "text",
+        "text": "incorporation of OT distance, mentioned in Sec. 3.3, can slightly improve the classification accuracy and largely enhance the part detection performance. OT provides a better distance metric space for modeling the complex many-to-many correlation between concept features and patch features, compared to the direct dot product similarity used in the baseline model.",
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+        "type": "text",
+        "text": "Effect of prior distribution modeling (Prior). The OT design above, setting the two prior distributions  $\\theta$  and  $\\gamma$  as a uniform distribution. To mitigate the shortcut learning brought by high occurrence between concept and background and between concept and concept, we add the background penalty patch set prior and the co-occurrence penalty concept set prior, mentioned in Sec. 3.4. Comparing the second and third rows of Table. 3, it demonstrates that these two prior distributions can further improve the classification and interpretability.",
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+    {
+        "type": "text",
+        "text": "Effect of local representation disentanglement (LrD). After integrating the local representation disentanglement into the baseline (the fourth row of Table. 3), the improvements are larger than a single incorporation of OT distance (the second row of Table. 3). The overall DOT-CBM, with a combination of the OT, Prior, and LrD, yields more improvements than individual modules alone.",
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+    {
+        "type": "text",
+        "text": "Qualitative results. Fig. 4 has shown a qualitative comparison between our method and the baseline methods Vanilla-CBM and CoopCBM. It is observed that our method is able to more accurately locate the region of the",
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+    {
+        "type": "text",
+        "text": "concept in the original image compared to the baseline methods. Meanwhile, We also present qualitative results by sequentially ablating each component of our framework. When the local representation disentanglement is ablated, the model's localization accuracy decreases to some extent. Further removal of the priors leads to the emergence of part-background spurious correlations. When the OT design is removed, the model produces incorrect localization results.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion.",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we introduced the Disentangled Optimal Transport Concept Bottleneck Model (DOT-CBM) to address key limitations in existing Concept Bottleneck Models. While CBMs offer interpretable models by mapping image features to human-understandable concepts, they suffer from misalignment between the image and concept, leading to spurious correlations that hinder both interpretability and generalization. To overcome these challenges, DOT-CBM introduces a disentangled optimal transport framework that ensures fine-grained alignment between image patches and corresponding textual concepts, thereby providing a more robust and interpretable model. By employing a dual penalty system, we mitigate the overfitting problem caused by data bias. Empirical results demonstrate that DOT-CBM outperforms previous CBM variants in both classification accuracy and interpretability, offering an effective solution to the problem of visual-concept spurious correlation.",
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+        "type": "page_number",
+        "text": "30206",
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+    {
+        "type": "text",
+        "text": "6. Acknowledgement",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work was supported in part by the National Natural Science Foundation of China under Grant U21B2006; in part by Shaanxi Youth Innovation Team Project; in part by the Fundamental Research Funds for the Central Universities QTZX24003 and QTZX22160; in part by the 111 Project under Grant B18039; Hao Zhang acknowledges the support of NSFC (62301384); Excellent Young Scientists Fund (Overseas); Foundation of National Key Laboratory of Radar Signal Processing under Grant JKW202308. Zhengjue Wang acknowledges the support of NSFC (62301407).",
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+        "type": "text",
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